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Exercises Equations and inequalities

Example 4 from Algebra and Trigonometry, 2.1 The Rectangular Coordinate Systems and Graphs

Finding the Intercepts of the Given Equation

Find the intercepts of the equation $y = −3 x - 4.$ Then sketch the graph using only the intercepts.

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
Set $y = 0$ to find the x-intercept.

$\begin{array}{l} y = −3 x - 4 \\ 0 = −3 x - 4 \\ 4 = −3 x \\ - \frac{4}{3} = x \\ (- \frac{4}{3}, 0) x −intercept \end{array}$
Set $x = 0$ to find the y-intercept.

$\begin{array}{l} y = −3 x - 4 \\ y = −3 (0) - 4 \\ y = −4 \\ (0, −4) y −intercept \end{array}$
Plot both points, and draw a line passing through them as in Figure 12.

Figure 12

Your turn

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

Find the intercepts of the equation and sketch the graph: $y = - \frac{3}{4} x + 3.$

How did it go?

PreviousUsing a Graphing Utility to Graph an Equation Next Finding the Distance between Two Points

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.1, 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.