Question

Write the equation perpendicular to y = 2x +1 and goes through the point (4, -1)

Answer 1

Answer:

y = -1/2x + 1

Step-by-step explanation:

A line is in the form y = mx + b. You need to know m and b.

m is for slope.

b is the y-intercept.

x and y are points on the line.

Perpendicular equations have slopes that are negative reciprocals of each other. This means that in fraction form, the top and bottom numbers are switched and the negative/positive signs are opposite.

In y = 2x + 1, the slope is 2. It's the same as 2/1. Switch the top and bottom number and change the sign. The slope for the equation you are finding is m = -1/2.

Substitute m for -1/2. y = -1/2(x) + b

A point is in the form (x, y). If a line passes through (4, -1) it can be used in the line's equation. Substitute x for 4 and y for -1.

y = -1/2(x) + b

-1 = (-1/2)(4) + b    Simplify

-1 = -4/2 + b     Reduce the fraction

-1 = -2 + b     Isolate b. Add 2 to both sides.

-1 + 2 = b

b = 1

The line uses m= -1/2 and b=1.

y = -1/2x + 1