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Example 5 from Algebra and Trigonometry, 4.1 Linear Functions

Writing an Equation for a Linear Function

Write an equation for a linear function given a graph of $f$ shown in Figure 8.

This figure shows an increasing function graphed on an x y coordinate plane. The x axis is labeled from negative 10 to 10. The y axis is labeled from negative 10 to 10. The function passes through the points (0, 2) and (-2, -4). These points are not labeled on this graph.

Figure 8

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
Identify two points on the line, such as $(0, 2)$ and $(−2, −4) .$ Use the points to calculate the slope.
$\begin{matrix} m & = & \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = & \frac{−4 - 2}{−2 - 0} \\ = & \frac{−6}{−2} \\ = & 3 \end{matrix}$
Substitute the slope and the coordinates of one of the points into the point-slope form.

$\begin{matrix} y - y_{1} & = & m (x - x_{1}) \\ y - (−4) & = & 3 (x - (−2)) \\ y + 4 & = & 3 (x + 2) \end{matrix}$
We can use algebra to rewrite the equation in the slope-intercept form.

$\begin{matrix} y + 4 & = & 3 (x + 2) \\ y + 4 & = & 3 x + 6 \\ y & = & 3 x + 2 \end{matrix}$

How did it go?

PreviousFinding the Population Change from a Linear Function Next Writing an Equation for a Linear Cost Function

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.