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.

y=-2x+2

Step-by-step 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.