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Exercises Graphs and straight lines

Example 4.10 from Elementary Algebra, 4.2 Graph Linear Equations in Two Variables

Graph Linear Equations in Two Variables: example 4.10

The graph of $y = 2 x - 3$ is shown.

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line has a positive slope and goes through the y-axis at the (0, negative 3). The line is labeled with the equation y equals 2x negative 3.

For each ordered pair, decide:

ⓐ Is the ordered pair a solution to the equation?
ⓑ Is the point on the line?

A $(0, −3)$ B $(2, −3)$ C $(2, −3)$ D $(−1, −5)$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Substitute the x- and y- values into the equation to check if the ordered pair is a solution to the equation.
1. ⓐ
2. ⓑ Plot the points A $(0, 3)$ , B $(3, 3)$ , C $(2, −3)$ , and D $y = 2 x - 3$ .
The points $y = 3 x - 1$ , $(3, 3)$ , and $(−1, −5)$ are on the line $y = 2 x - 3$ , and the point $(2, −3)$ is not on the line.

The points that are solutions to $y = 2 x - 3$ are on the line, but the point that is not a solution is not on the line.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the graph of $y = 3 x - 1$ to decide whether each ordered pair is:

a solution to the equation.
on the line.

ⓐ $(0, −1)$ ⓑ $(2, 5)$

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the point (negative 2, negative 7) and for every 3 units it goes up, it goes one unit to the right. The line is labeled with the equation y equals 3x minus 1.

How did it go?

PreviousUse the Rectangular Coordinate System: example 4.9 Next Graph Linear Equations in Two Variables: example 4.11

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 4.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.