Question

What are the x- and y-intercepts of a line that passes through (5, 18) with a slope of 2?

Answer 1

The point-slope form:

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

We have the point (5, 18) and m = 2.

Substitute:

`y-18=2(x-5)`

The slope-intercept form is y = mx + b

`y-18=(2)(x)+(2)(-5)\\y-18=2x-10\qquad|+18\\y=2x+8`

x-intercept:

substitute y = 0 to the equation of the function:

`0=2x+8\qquad|-8\\-8=2x\qquad|:2\\x=-4`

y-intercept:

substitute x = 0 to the equation of the function:

`y=2(0)+8\\y=8`

Answer:

x-intercept = -4

y-intercept = 8