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Exercises Graphs and straight lines

Example 11 from Algebra and Trigonometry, 4.1 Linear Functions

Graphing by Plotting Points

Graph $f (x) = - \frac{2}{3} x + 5$ by plotting points.

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.

Solution
Begin by choosing input values. This function includes a fraction with a denominator of 3, so let’s choose multiples of 3 as input values. We will choose 0, 3, and 6.

Evaluate the function at each input value, and use the output value to identify coordinate pairs.

$\begin{matrix} x = 0 & f (0) = - \frac{2}{3} (0) + 5 = 5 \Rightarrow (0, 5) \\ x = 3 & f (3) = - \frac{2}{3} (3) + 5 = 3 \Rightarrow (3, 3) \\ x = 6 & f (6) = - \frac{2}{3} (6) + 5 = 1 \Rightarrow (6, 1) \end{matrix}$
Plot the coordinate pairs and draw a line through the points. Figure 11 represents the graph of the function $f (x) = - \frac{2}{3} x + 5.$

Figure 11 The graph of the linear function $f (x) = - \frac{2}{3} x + 5.$

Your turn

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

Graph $f (x) = - \frac{3}{4} x + 6$ by plotting points.

How did it go?

PreviousUsing Tabular Form to Write an Equation for a Linear Function Next Graphing by Using the y-intercept and Slope

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 4.1, 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.