Question

Write an equation in​ slope-intercept form of the line satisfying the given conditions.

The line passes through ​(5​,-8​) and is perpendicular to the line whose equation is x-2y=7.

Answer 1

y=-2x+2

Explanation:

Given line is-

x-2y=7

we know,

equation of line perpendicular to ax+by=c is bx-ay=k

So, equation of line perpendicular to x-2y=7

is given by -2x-y=k

Now, the line -2x-y=k passes through (5,-8)

So, we get

-2(5)-(-8)=k

or, -10+8=k

or, -2=k

So, k=-2

Using the k value we get,

Equation of the line is-

-2x-y=-2

multiplying by -1

2x+y=2

or, y=-2x+2

This is the slope intercept form of the line.