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Exercícios de gráficos e retas · Physics Playground

ExercíciosMatemática

Gráficos e retas

140 problemas com soluções resolvidas, de Prealgebra, Elementary Algebra, Algebra and Trigonometry e Precalculus.

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Aprenda antes: Retas e Inclinação

Prealgebra11.1 Use the Rectangular Coordinate System

Exemplo 11.1Use the map in Figure 11.2. ⓐ Find the grid section of the Residence Halls. ⓑ What is located in grid section 4C?Mais um parecido para tentar
Exemplo 11.2Plot (1,3) and (3,1) in the same rectangular coordinate system.Mais um parecido para tentar
Exemplo 11.3Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located: ⓐ(−1,3)ⓑ(−3,−4)ⓒ(2,−3)ⓓ(3,5/2)Mais um parecido para tentar
Exemplo 11.4Plot each point: ⓐ(−5,2)ⓑ(−5,−2)ⓒ(5,2)ⓓ(5,−2)Mais um parecido para tentar
Exemplo 11.5Plot each point on a coordinate grid: ⓐ(0,5)ⓑ(4,0)ⓒ(−3,0)ⓓ(0,0)ⓔ(0,−1)Mais um parecido para tentar
Exemplo 11.6Name the ordered pair of each point shown:Com figuraMais um parecido para tentar
Exemplo 11.8Determine which ordered pairs are solutions of the equation x+4y=8: ⓐ(0,2)ⓑ(2,−4)ⓒ(−4,3)Mais um parecido para tentar
Exemplo 11.9Determine which ordered pairs are solutions of the equation. y=5x−1: ⓐ(0,−1)ⓑ(1,4)ⓒ(−2,−7)Mais um parecido para tentar
Exemplo 11.10Complete the table to find three solutions to the equation y=4x−2: y=4x−2 x y (x,y) 0 −1 2Mais um parecido para tentar
Exemplo 11.11Complete the table to find three solutions to the equation 5x−4y=20: 5x−4y=20 x y (x,y) 0 0 5Mais um parecido para tentar
Exemplo 11.12Find a solution to the equation 3x+2y=6.Mais um parecido para tentar
Exemplo 11.13Find three more solutions to the equation 3x+2y=6.Mais um parecido para tentar
Exemplo 11.14Find three solutions to the equation x−4y=8.Mais um parecido para tentar

Prealgebra11.2 Graphing Linear Equations

Exemplo 11.15The graph of y=2x−3 is shown below. For each ordered pair decide ⓐ Is the ordered pair a solution to the equation? ⓑ Is the point on the line? (a) (0,3)(b) (3,−3)(c) (2,−3) (d) (−1,−5)Com figuraMais um parecido para tentar
Exemplo 11.16Graph the equation y=−3x.Mais um parecido para tentar
Exemplo 11.17Graph the equation y=1/2x+3.Mais um parecido para tentar
Exemplo 11.18Graph the equation x+y=5.Mais um parecido para tentar
Exemplo 11.19Graph the equation 3x+y=−1.Mais um parecido para tentar
Exemplo 11.20Graph the equation x=2. What type of line does it form?Mais um parecido para tentar
Exemplo 11.21Graph the equation y=−1.Mais um parecido para tentar
Exemplo 11.22Graph y=−3x and y=−3 in the same rectangular coordinate system.Mais um parecido para tentar

Prealgebra11.3 Graphing with Intercepts

Exemplo 11.23Find the x- andy-intercepts of each line: ⓐx+2y=4 ⓑ3x−y=6 ⓒx+y=−5Com figuraMais um parecido para tentar
Exemplo 11.24Find the intercepts of 2x+y=6Mais um parecido para tentar
Exemplo 11.25Find the intercepts of 4x−3y=12.Mais um parecido para tentar
Exemplo 11.26Graph −x+2y=6 using intercepts.Mais um parecido para tentar
Exemplo 11.27Graph 4x−3y=12 using intercepts.Mais um parecido para tentar
Exemplo 11.28Graph y=5x using the intercepts.Mais um parecido para tentar
Exemplo 11.29Identify the most convenient method to graph each line: ⓐy=−3ⓑ4x−6y=12 ⓒx=2ⓓy=2/5x−1Mais um parecido para tentar

Prealgebra11.4 Understand Slope of a Line

Exemplo 11.30What is the slope of the line on the geoboard shown?Com figuraMais um parecido para tentar
Exemplo 11.32Use a geoboard to model a line with slope 1/2.Mais um parecido para tentar
Exemplo 11.33Use a geoboard to model a line with slope (−1)/4,Mais um parecido para tentar
Exemplo 11.34Find the slope of the line shown:Com figuraMais um parecido para tentar
Exemplo 11.37Find the slope of each line: ⓐx=8ⓑy=−5Mais um parecido para tentar
Exemplo 11.38Find the slope of the line between the points (1,2) and (4,5).Mais um parecido para tentar
Exemplo 11.39Find the slope of the line through the points (−2,−3) and (−7,4).Mais um parecido para tentar
Exemplo 11.40Graph the line passing through the point (1,−1) whose slope is m=3/4.Mais um parecido para tentar
Exemplo 11.41Graph the line with y-intercept (0,2) and slope m=−2/3.Mais um parecido para tentar
Exemplo 11.42Graph the line passing through the point (−1,−3) whose slope is m=4.Mais um parecido para tentar
Exemplo 11.43The pitch of a building’s roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is the…Com figuraMais um parecido para tentar
Exemplo 11.44Sewage pipes must slope down 1/4 inch per foot in order to drain properly. What is the required slope?Com figuraMais um parecido para tentar

Elementary Algebra4.1 Use the Rectangular Coordinate System

Exemplo 4.1Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located: ⓐ (−5,4) ⓑ (−3,−4) ⓒ (2,−3) ⓓ (−2,3) ⓔ (3,5/2).Mais um parecido para tentar
Exemplo 4.2Plot each point: ⓐ (0,5) ⓑ (4,0) ⓒ (−3,0) ⓓ (0,0) ⓔ (0,−1).Mais um parecido para tentar
Exemplo 4.3Name the ordered pair of each point shown in the rectangular coordinate system.Com figuraMais um parecido para tentar
Exemplo 4.4Determine which ordered pairs are solutions to the equation x+4y=8. ⓐ (0,2) ⓑ (2,−4) ⓒ (−4,3)Mais um parecido para tentar
Exemplo 4.5Which of the following ordered pairs are solutions to the equation y=5x−1? ⓐ (0,−1) ⓑ (1,4) ⓒ (−2,−7)Mais um parecido para tentar
Exemplo 4.6Complete Table 4.4 to find three solutions to the equation y=4x−2. y=4x−2 x y (x,y) 0 −1 2 Table 4.4Mais um parecido para tentar
Exemplo 4.7Complete Table 4.6 to find three solutions to the equation 5x−4y=20. 5x−4y=20 x y (x,y) 0 0 5 Table 4.6Mais um parecido para tentar
Exemplo 4.8Find three solutions to the equation y=−3x+2.Mais um parecido para tentar
Exemplo 4.9Find three solutions to the equation 3x+2y=6.Mais um parecido para tentar

Elementary Algebra4.2 Graph Linear Equations in Two Variables

Exemplo 4.10The graph of y=2x−3 is shown. For each ordered pair, decide: ⓐ Is the ordered pair a solution to the equation? ⓑ Is the point on the line? A (0,−3) B (3,3) C (2,−3) D (−1,−5)Com figuraMais um parecido para tentar
Exemplo 4.11Graph the equation y=2x+1 by plotting points.Mais um parecido para tentar
Exemplo 4.15Graph the equation 2x−3y=6.Mais um parecido para tentar
Exemplo 4.16Graph the equation x=2.Mais um parecido para tentar

Elementary Algebra4.3 Graph with Intercepts

Exemplo 4.19Find the x- and y- intercepts on each graph.Com figuraMais um parecido para tentar
Exemplo 4.22Graph –x+2y=6 using the intercepts.Mais um parecido para tentar
Exemplo 4.23Graph 4x–3y=12 using the intercepts.Mais um parecido para tentar

Elementary Algebra4.4 Understand Slope of a Line

Exemplo 4.33Use the slope formula to find the slope of the line between the points (1,2) and (4,5).Mais um parecido para tentar
Exemplo 4.34Use the slope formula to find the slope of the line through the points (−2,−3) and (−7,4).Mais um parecido para tentar
Exemplo 4.36Graph the line with y-intercept 2 whose slope is m=−2/3.Mais um parecido para tentar
Exemplo 4.38The ‘pitch’ of a building’s roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is…Com figuraMais um parecido para tentar
Exemplo 4.39Have you ever thought about the sewage pipes going from your house to the street? They must slope down 1/4 inch per foot in order to drain properly. What is the required slope?Com figuraMais um parecido para tentar

Elementary Algebra4.5 Use the Slope–Intercept Form of an Equation of a Line

Exemplo 4.40Use the graph to find the slope and y-intercept of the line, y=2x+1. Compare these values to the equationy=mx+b.Mais um parecido para tentar
Exemplo 4.41Identify the slope and y-intercept of the line with equation y=−3x+5.Mais um parecido para tentar
Exemplo 4.42Identify the slope and y-intercept of the line with equation x+2y=6.Mais um parecido para tentar
Exemplo 4.43Graph the line of the equation y=4x−2 using its slope and y-intercept.Mais um parecido para tentar
Exemplo 4.44Graph the line of the equation y=−x+4 using its slope and y-intercept.Mais um parecido para tentar
Exemplo 4.45Graph the line of the equation y=−2/3x−3 using its slope and y-intercept.Mais um parecido para tentar
Exemplo 4.46Graph the line of the equation 4x−3y=12 using its slope and y-intercept.Mais um parecido para tentar
Exemplo 4.47Graph the line of the equation y=0.2x+45 using its slope and y-intercept.Mais um parecido para tentar
Exemplo 4.48Determine the most convenient method to graph each line. ⓐ y=−6 ⓑ 5x−3y=15 ⓒ x=7 ⓓ y=2/5x−1.Mais um parecido para tentar
Exemplo 4.49The equation F=9/5C+32 is used to convert temperatures, C, on the Celsius scale to temperatures, F, on the Fahrenheit scale. ⓐ Find the Fahrenheit temperature for a Celsius temperature of 0. ⓑ Find the Fahrenheit…Mais um parecido para tentar
Exemplo 4.50Stella has a home business selling gourmet pizzas. The equation C=4p+25 models the relation between her weekly cost, C, in dollars and the number of pizzas, p, that she sells. ⓐ Find Stella’s cost for a week when she…Mais um parecido para tentar
Exemplo 4.51Use slopes and y-intercepts to determine if the lines 3x−2y=6 and y=3/2x+1 are parallel.Mais um parecido para tentar
Exemplo 4.52Use slopes and y-intercepts to determine if the lines y=−4 and y=3 are parallel.Mais um parecido para tentar
Exemplo 4.53Use slopes and y-intercepts to determine if the lines x=−2 and x=−5 are parallel.Mais um parecido para tentar
Exemplo 4.54Use slopes and y-intercepts to determine if the lines y=2x−3 and −6x+3y=−9 are parallel. You may want to graph these lines, too, to see what they look like.Mais um parecido para tentar
Exemplo 4.55Use slopes to determine if the lines, y=−5x−4 and x−5y=5 are perpendicular.Mais um parecido para tentar
Exemplo 4.56Use slopes to determine if the lines, 7x+2y=3 and 2x+7y=5 are perpendicular.Mais um parecido para tentar

Elementary Algebra4.6 Find the Equation of a Line

Exemplo 4.57Find an equation of a line with slope −7 and y-intercept (0,−1).Mais um parecido para tentar
Exemplo 4.58Find the equation of the line shown.Com figuraMais um parecido para tentar
Exemplo 4.59Find an equation of a line with slope m=2/5 that contains the point (10,3). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.60Find an equation of a line with slope m=−1/3 that contains the point (6,−4). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.61Find an equation of a horizontal line that contains the point (−1,2). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.62Find an equation of a line that contains the points (5,4) and (3,6). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.63Find an equation of a line that contains the points (−3,−1) and (2,−2). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.64Find an equation of a line that contains the points (−2,4) and (−2,−3). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.65Find an equation of a line parallel to y=2x−3 that contains the point (−2,1). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.66Find an equation of a line perpendicular to y=2x−3 that contains the point (−2,1). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.67Find an equation of a line perpendicular to x=5 that contains the point (3,−2). Write the equation in slope–intercept form.Mais um parecido para tentar
Exemplo 4.68Find an equation of a line that is perpendicular to y=−4 that contains the point (−4,2). Write the equation in slope–intercept form.Mais um parecido para tentar

Elementary Algebra4.7 Graphs of Linear Inequalities

Exemplo 4.69Determine whether each ordered pair is a solution to the inequality y>x+4: ⓐ (0,0) ⓑ (1,6) ⓒ (2,6) ⓓ (−5,−15) ⓔ (−8,12)Mais um parecido para tentar
Exemplo 4.70The boundary line shown is y=2x−1. Write the inequality shown by the graph.Com figuraMais um parecido para tentar
Exemplo 4.71The boundary line shown is 2x+3y=6. Write the inequality shown by the graph.Com figuraMais um parecido para tentar
Exemplo 4.72Graph the linear inequality y≥3/4x−2.Mais um parecido para tentar
Exemplo 4.73Graph the linear inequality x−2y<5.Mais um parecido para tentar
Exemplo 4.74Graph the linear inequality y≤−4x.Mais um parecido para tentar
Exemplo 4.75Graph the linear inequality y>3.Mais um parecido para tentar

Algebra and Trigonometry4.1 Linear Functions

Exemplo 1Using a Linear Function to Find the Pressure on a DiverThe pressure, P, in pounds per square inch (PSI) on the diver in Figure 4 depends upon her depth below the water surface, d, in feet. This relationship may be modeled by the equation, P(d)=0.434d+14.696. Restate this…Com figura
Exemplo 2Deciding Whether a Function Is Increasing, Decreasing, or ConstantSome recent studies suggest that a teenager sends an average of 60 texts per day3. For each of the following scenarios, find the linear function that describes the relationship between the input value and the output…
Exemplo 3Finding the Slope of a Linear FunctionIf f(x) is a linear function, and (3,−2) and (8,1) are points on the line, find the slope. Is this function increasing or decreasing?Mais um parecido para tentar
Exemplo 4Finding the Population Change from a Linear FunctionThe population of a city increased from 23,400 to 27,800 between 2008 and 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.Mais um parecido para tentar
Exemplo 5Writing an Equation for a Linear FunctionWrite an equation for a linear function given a graph of f shown in Figure 8. Figure 8Com figura
Exemplo 6Writing an Equation for a Linear Cost FunctionSuppose Ben starts a company in which he incurs a fixed cost of $1,250 per month for the overhead, which includes his office rent. His production costs are $37.50 per item. Write a linear function C where C( x) is…
Exemplo 7Writing an Equation for a Linear Function Given Two PointsIf f is a linear function, with f(3)=−2, and f(8)=1, find an equation for the function in slope-intercept form.Mais um parecido para tentar
Exemplo 8Using a Linear Function to Determine the Number of Songs in a Music CollectionMarcus currently has 200 songs in his music collection. Every month, he adds 15 new songs. Write a formula for the number of songs, N, in his collection as a function of time, t, the number of months. How many songs…
Exemplo 9Using a Linear Function to Calculate Salary Based on CommissionWorking as an insurance salesperson, Ilya earns a base salary plus a commission on each new policy. Therefore, Ilya’s weekly income I, depends on the number of new policies, n, he sells during the week. Last week he…
Exemplo 10Using Tabular Form to Write an Equation for a Linear FunctionTable 1 relates the number of rats in a population to time, in weeks. Use the table to write a linear equation. number of weeks, w 0 2 4 6 number of rats, P(w) 1000 1080 1160 1240 Table 1Mais um parecido para tentar
Exemplo 11Graphing by Plotting PointsGraph f(x)=−2/3 x+5 by plotting points.Mais um parecido para tentar
Exemplo 12Graphing by Using the y-intercept and SlopeGraph f(x)=−2/3 x+5 using the y-intercept and slope.Mais um parecido para tentar
Exemplo 13Graphing by Using TransformationsGraph f(x)=1/2 x−3 using transformations.Mais um parecido para tentar
Exemplo 14Matching Linear Functions to Their GraphsMatch each equation of the linear functions with one of the lines in Figure 19. ⓐ f(x)=2x+3 ⓑ g(x)=2x−3 ⓒ h(x)=−2x+3 ⓓ j(x)=1/2x+3 Figure 19Com figura
Exemplo 15Finding an x-interceptFind the x-intercept of f(x)=1/2 x−3.Mais um parecido para tentar
Exemplo 16Writing the Equation of a Horizontal LineWrite the equation of the line graphed in Figure 26. Figure 26Com figura
Exemplo 17Writing the Equation of a Vertical LineWrite the equation of the line graphed in Figure 27. Figure 27Com figura
Exemplo 18Identifying Parallel and Perpendicular LinesGiven the functions below, identify the functions whose graphs are a pair of parallel lines and a pair of perpendicular lines. f(x) = 2x+3 h(x) = −2x+2 g(x) = 1/2 x−4 j(x) = 2x−6
Exemplo 19Finding a Line Parallel to a Given LineFind a line parallel to the graph of f(x)=3x+6 that passes through the point (3,0).
Exemplo 20Finding the Equation of a Perpendicular LineFind the equation of a line perpendicular to f(x)=3x+3 that passes through the point (3,0).Mais um parecido para tentar
Exemplo 21Finding the Equation of a Line Perpendicular to a Given Line Passing through a PointA line passes through the points (−2,6) and (4,5). Find the equation of a perpendicular line that passes through the point (4,5).Mais um parecido para tentar

Algebra and Trigonometry4.2 Modeling with Linear Functions

Exemplo 1Using a Linear Model to Investigate a Town’s PopulationA town’s population has been growing linearly. In 2004, the population was 6,200. By 2009, the population had grown to 8,100. Assume this trend continues. ⓐPredict the population in 2013. ⓑIdentify the year in which…Mais um parecido para tentar
Exemplo 2Using a Diagram to Model Distance WalkedAnna and Emanuel start at the same intersection. Anna walks east at 4 miles per hour while Emanuel walks south at 3 miles per hour. They are communicating with a two-way radio that has a range of 2 miles. How long…
Exemplo 3Using a Diagram to Model Distance Between CitiesThere is a straight road leading from the town of Westborough to Agritown 30 miles east and 10 miles north. Partway down this road, it junctions with a second road, perpendicular to the first, leading to the town of…Mais um parecido para tentar
Exemplo 4Building a System of Linear Models to Choose a Truck Rental CompanyJamal is choosing between two truck-rental companies. The first, Keep on Trucking, Inc., charges an up-front fee of $20, then 59 cents a mile. The second, Move It Your Way, charges an up-front fee of $16, then 63…

Algebra and Trigonometry4.3 Fitting Linear Models to Data

Exemplo 1Using a Scatter Plot to Investigate Cricket ChirpsTable 1 shows the number of cricket chirps in 15 seconds, for several different air temperatures, in degrees Fahrenheit5. Plot this data, and determine whether the data appears to be linearly related. 5Selected data…
Exemplo 2Finding a Line of Best FitFind a linear function that fits the data in Table 1 by “eyeballing” a line that seems to fit.
Exemplo 3Understanding Interpolation and ExtrapolationUse the cricket data from Table 1 to answer the following questions: ⓐWould predicting the temperature when crickets are chirping 30 times in 15 seconds be interpolation or extrapolation? Make the prediction, and…Mais um parecido para tentar
Exemplo 4Finding a Least Squares Regression LineFind the least squares regression line using the cricket-chirp data in Table 2.
Exemplo 5Finding a Correlation CoefficientCalculate the correlation coefficient for cricket-chirp data in Table 1.
Exemplo 6Using a Regression Line to Make PredictionsGasoline consumption in the United States has been steadily increasing. Consumption data from 1994 to 2004 is shown in Table 3.8 Determine whether the trend is linear, and if so, find a model for the data. Use the…Com figuraMais um parecido para tentar

Precalculus2.1 Linear Functions

Exemplo 5Writing Linear Equations Using a Point and the SlopeWrite the point-slope form of an equation of a line with a slope of 3 that passes through the point ( 6,–1). Then rewrite it in the slope-intercept form.Mais um parecido para tentar
Exemplo 6Writing Linear Equations Using Two PointsWrite the point-slope form of an equation of a line that passes through the points (5, 1) and (8, 7). Then rewrite it in the slope-intercept form.Mais um parecido para tentar
Exemplo 7Writing an Equation for a Linear FunctionWrite an equation for a linear function given a graph of f shown in Figure 10. Figure 10Com figura
Exemplo 8Writing an Equation for a Linear Cost FunctionSuppose Ben starts a company in which he incurs a fixed cost of $1,250 per month for the overhead, which includes his office rent. His production costs are $37.50 per item. Write a linear function C where C(x) is the…
Exemplo 11Using a Linear Function to Calculate Salary Plus CommissionWorking as an insurance salesperson, Ilya earns a base salary plus a commission on each new policy. Therefore, Ilya’s weekly income, I, depends on the number of new policies, n, he sells during the week. Last week he…
Exemplo 12Using Tabular Form to Write an Equation for a Linear FunctionTable 1 relates the number of rats in a population to time, in weeks. Use the table to write a linear equation. w, number of weeks 0 2 4 6 P(w), number of rats 1000 1080 1160 1240 Table 1Mais um parecido para tentar

Precalculus2.2 Graphs of Linear Functions

Exemplo 4Matching Linear Functions to Their GraphsMatch each equation of the linear functions with one of the lines in Figure 9. ⓐ f(x)=2x+3 ⓑ g(x)=2x−3 ⓒ h(x)=−2x+3 ⓓ j(x)=1/2x+3 Figure 9Com figura
Exemplo 6Writing the Equation of a Horizontal LineWrite the equation of the line graphed in Figure 15. Figure 15Com figura
Exemplo 7Writing the Equation of a Vertical LineWrite the equation of the line graphed in Figure 16. Figure 16Com figura
Exemplo 12Finding a Point of Intersection AlgebraicallyFind the point of intersection of the lines h(t)=3t−4 and j(t)=5−t.Mais um parecido para tentar
Exemplo 13Finding a Break-Even PointA company sells sports helmets. The company incurs a one-time fixed cost for $250,000. Each helmet costs $120 to produce, and sells for $140. ⓐ Find the cost function, C, to produce x helmets, in dollars. ⓑ Find the…

Precalculus2.4 Fitting Linear Models to Data

Exemplo 4Finding a Least Squares Regression LineFind the least squares regression line using the cricket-chirp data in Table 1.