Question

A line goes through the points (-6, -8) and (12, 7).

a) What is the slope of the line? Show your work
b) Write the equation of the line in point-slope form. Show your work
c) Write the equation of the line in slope-intercept form. Show your work.

Answer 1

The formula of a slope:

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

We have (-6, -8), (12, 7).

Substitute:

`m=(7-(-8))/(12-(-6))=(7+8)/(12+6)=(15)/(18)=(5)/(6)`

The slope-point form:

`y-y_1=m(x-x_1)`

We have m = 5/6 and (12, 7).

Substitute:

`y-7=(5)/(6)(x-12)`

The slope-intercept form:

`y=mx+b`

`y-7=(5)/(6)(x-12)\\\\y-7=(5)/(6)x-(5)/(6)\cdot12}\\\\y-7=(5)/(6)x-(5)/(1)\cdot2\\\\y-7=(5)/(6)x-10\qquad|+7\\\\y=(5)/(6)x-3`