Question

Find the equation of the line. Use exact numbers. Y xt у 9 8 7 8 6 5 4 3+ 2 2 x -9-8-7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 -2- -3- -4 -5+ -67 -7 -87 -9+

Answer 1

Let's take 2 points from the graph:

$\begin{gathered} (x_1,y_1)=(6,0) \\ (x_2,y_2)=(0,-3) \end{gathered}$

We can find the equation of a line using the formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

We will substitute the points and arrange the equation in y = mx + b form. Shown below:

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-0=\frac{-3-0}{0-6}(x-6) \\ y=\frac{-3}{-6}(x-6) \\ y=\frac{1}{2}(x-6) \\ y=\frac{1}{2}x-\frac{1}{2}(6) \\ y=\frac{1}{2}x-3 \end{gathered}$

The equation of the line is:

$y=\frac{1}{2}x-3$