Question

Write the equation of the line that passes through the points (8, -1) and (2, -5) inpoint-slope form.

Answer 1

First, we find the slope using the given points and the formula below

`m=(y_2-y_1)/(x_2-x_1)=(-5-(-1))/(2-8)=(-5+1)/(-6)=(-4)/(-6)=(2)/(3)`

Then, we use the point-slope formula to find the equation

`y-y_1=m(x-x_1)_{}`

Let's replace the point (8, -1) and the slope 2/3.

`\begin{gathered} y-(-1)=(2)/(3)(x-8) \\ y+1=(2)/(3)x-(16)/(3) \\ y=(2)/(3)x-(16)/(3)-1 \\ y=(2)/(3)x+(-16-3)/(3) \\ y=(2)/(3)x-(19)/(3) \end{gathered}`

Hence, the equation in point-slope form is

`y+1=(2)/(3)(x-8)`