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=(y_2-y_1)/(x_2-x_1) \\ =(-4-8)/(1-(-1)) \\ =(-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).