Question

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Answer 1

Option A

The equation of the perpendicular line in slope-intercept-form is
`y=(1)/(3)x`

Explanation:

Use the slope-intercept form to find the slope.

The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept.

Using the slope-intercept form, the slope is − 3 .

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

`m_(perpr)=-(1)/(-3)`

`m_(perpr)=(1)/(3)`

Find the equation of the perpendicular line using the point-slope formula.

Use the slope
`(1)/(3)` and a given point ( − 15 , − 5 ) to substitute for
`x_(1)` and
`y_(1)` in the point-slope form
`y-y_1=m(x-x_1)`.

`y-(-5)=(1)/(3) *(x-(-15))`

Simplify the equation and keep it in point-slope form.

`y+5=(1)/(3) *(x+15)`

Write in y = m x + b form.

Solve for y .

`y+5=(1)/(3) *(x+15)`

`y=(x)/(3)`

`y=(1)/(3)x`