Question

What is the equation of the line that is perpendicular to the line y=2x+5 and passes through the point (-4, -2)?

A. y = 2x + 6, B. y= -1/2x, C. y= -1/2x+2, D. y = 2x - 6
help plz anyone

Answer 1

The equation of the line that is perpendicular to y = 2x + 5 and passes through the point (-4, -2) is y = -1/2x + 1.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to determine the negative reciprocal of the original line's slope and then use the given point to find the y-intercept.

The given line is y = 2x + 5. The slope of this line is 2, so the slope of the perpendicular line will be the negative reciprocal, which is -1/2. Using the point (-4, -2) and the slope -1/2, we can plug these values into the point-slope form of a linear equation to find the equation of the perpendicular line.

The equation of the line that is perpendicular to y = 2x + 5 and passes through the point (-4, -2) is y = -1/2x + 1.

Answer 2

The equation is y = -1/4x - 4.

Point Slope Form: y - y1 = m(x - x1)
Given: (-4,-2) and y = 2x + 5

When you are given a line that is perpendicular, flip the slope upside down and change it to it's opposite (negative to positive etc).

Slope: -1/2

Now plug that and the point into the formula for PS form.

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