Question

Find an equation for the line perpendicular to y=−1/7x+2 with x-intercept at x = -7.

Write your answer in the form y=mx+b.

y=

Answer 1

`y=7x+49`

Explanation:

To find the slope of a line which is perpendicular to another line, you need to find the opposite reciprocal of the first line's slope.

To find the opposite, flip the slope's sign. Your original slope is
`-(1)/(7)`, so your opposite slope is positive
`(1)/(7)`.

To find the reciprocal, flip the fraction. This changes your slope from
`(1)/(7)` to
`(7)/(1)`, which may be written as just 7.

Therefore, your slope is 7.

To find your b term (your y-intercept) given that your x-intercept is -7, you can make use of point-slope form.

`y-y1=m(x-x1)`

(m=slope)

If your x-intercept is -7, then the point at which your line intersects the x-axis is (-7, 0).

`y-0=7(x-(-7))\\y=7(x+7)\\y=7x+49`