Question

What is the equation of the line that passes through (-1,8 and (1, -4)?

Answer 1

Using slope-intercept form, an equation of a line can be written as

$y=mx+c$

Find the slope using the two-point formula.

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-8}{1-(-1)} \\ =\frac{-12}{2} \\ =-6 \end{gathered}$

Substitute -6 for m into y = mx + c.

$y=-6x+c$

Now, to find the y-intercept,c, substitute any given point into the equation.

$\begin{gathered} 8=-6(-1)+c \\ 8=6+c \\ c=2 \end{gathered}$

Thus, y = -6x + 2, which is the required equation of the line passing through (-1,8) and (1,-4).