Question

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation: (-3,-2) y=x+2

Answer 1

Given :

A point ( -3 , -2 ).

An equation of a line, y = x + 2.

To Find :

An equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.

Solution :

Let, equation of new line is :

y = mx + c     ....1)

Here, m and c are slope and intercept respectively.

We know, product of slope of two line is -1 :

m( 1 ) = -1

m = -1

It is also given that point ( -3,-2 ) passes through this point.

Putting value of this point and slope in equation 1), we get :

$-2 = (-1)\times ( -3 ) + c\\\\c = -2 -3\\\\c = -5$

Therefore, the equation of line is : y = -x -5 .