Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those points in the picture below.

`(\stackrel{x_1}{-5}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-5)}}}\implies \cfrac{-12}{5+5}\implies \cfrac{-12}{10}\implies -\cfrac{6}{5}`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-5)})\implies y-4=-\cfrac{6}{5}(x+5) \\\\\\ y-4=-\cfrac{6}{5}x-6\implies y=-\cfrac{6}{5}x-2`

Answer 2

y = -6/5x - 2

Explanation:

The line intercepts the y-axis 2 below 0, and down 6 for every 5 to the right on the x-axis