Question

50 points
Write the equation of the line in slope-intercept form (picture here)

Answer 1

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

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-4 +8}{4 +4} \implies \cfrac{ 4 }{ 8 }\implies \cfrac{1}{2}`

`\begin{array}c \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}{(-8)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \implies y +8= \cfrac{1}{2} (x +4) \\\\\\ y+8=\cfrac{1}{2}x+2\implies {\LARGE \begin{array}{llll} y=\cfrac{1}{2}x-6 \end{array}}`

Answer 2

`f(x)=(1)/(2)x+-6` or y=1/2x+-6

Explanation:

You can use any two points on a line to find slope. For example, I used:

(x1, y1) 2, -5

(x2, y2) 4, -4

To find slope, the following formula is needed:

`m=(y_2-y_1)/(x_2-x_1)`

Input our values:

`m=((-4)-(-5))/(4-2)` which means m=1/2

b is equal to y-intercept which is -6

The equation is:

`y=(1)/(2)x+-6`