Question

What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.

Answer 1

Answer: y=(-1/2)x+5.5

Explanation:

y=2x+3

This equation is in the slope-intercept form y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

m=2

The slope of the perpendicular line is -1/2.

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

(y-4)=(-1/2)(x-3)

y-4=(-1/2)x+1.5

add 4 to both sides

4+y-4=(-1/2)x+1.5+4

y=(-1/2)x+5.5

Answer 2

y = -1/2x + 2

Explanation:

The slope of a perpendicular line will be the opposite reciprocal (opposite sign, and reciprocal)

The line's slope is 2, so the perpendicular line's slope will be -1/2.

Now, we know part of the equation: y = -1/2x + b

Plug in the point given:

5 = -1/2(-6) + b

5 = 3 + b

2 = b

Now, we can plug in b into the equation:

y = -1/2x + 2