Question

How to write an equation of a line that goes through the points (4, -8) and (-7, 3). I know how to find the slope but not the y-intercept.

Answer 1

To determine the equation of a line that passes through two given points (x₁,y₁), and (x₂,y₂), we can use the following formula:

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

Substituting:

$\begin{gathered} (x_1,y_1)=(4,-8), \\ (x_2,y_2)=(-7,3) \end{gathered}$

in the above formula, we get:

$y-(-8)=\frac{3-(-8)}{-7-4}(x-4).$

Simplifying the above result, we get:

$\begin{gathered} y+8=\frac{11}{-11}(x-4), \\ y+8=-1(x-4), \\ y+8=-x+4. \end{gathered}$

Finally, to determine the y-intercept we can take the above equation to its slope-intercept form (y=mx+b):

$\begin{gathered} y=-x+4-8, \\ y=-x-4. \end{gathered}$

Answer:

Equation:

$y=-x-4.$

y-intercept:

$-4.$