Which equation represents a line that is perpendicular to the line represented by 4x - 2y = 7 ?

Question

1. 2x + y = 4

2. -4y + 2x = 3

3. -6y = 3x - 24

4. x + y = -1

Answer 1

Hello!

First thing you should do here is rearrange the equation into slope-intercept form by solving for y.

4x - 2y = 7

+2y +2y (Add 2y to both sides of the equation)

4x = 2y + 7

-7 -7 (Subtract 7 from both sides of the equation)

4x - 7 = 2y

2 2 2 (Divide everything by 2 to get y by itself)

2x - 3.5 = y

y = 2x - 3.5 the equation we will be working with. In this form, we can easily see that the slope is 2x. For a line to be perpendicular to this line, the slope will be the negative inverse of 2x.

If we start with line y=mx+b a line perpendicular to this would be y = - 1/m x + b.

Since our line is y = 2x - 3.5, our perpendicular line will be y = - 1/2x +b.

Now, we need to rearrange our multiple choice options to be in slope intercept form for us to be able to compare and find the right answer.

1) 2x +y = 4

-2x -2x (Subtract 2x)

y = -2x + 4

2) -4y + 2x = 3

-2x -2x (Subtract 2x)

-4y = -2x +3 (Divide everything by -4 to get y by itself)

-4 -4 -4

y = 1/2x - 3/4

3) -6y= 3x -24 (Divide everything by -6)

-6 -6 -6

y = -1/2x + 4 This is our answer because it has the slope we are looking for -1/2x. This slope is the

negative inverse of the line we started with, 2x.

I hope this was helpful! Please feel free to reach out if you have more questions! Good luck!

Holly Anderson

Answer 2

Hello, Natalia,

Let's rewrite the equation to put it into standard form of y = mx + b. This format allows us to study the slope, m, which is the key factor in determining the overall form of the line.

-2y = -4x + 7

y = (-4/-2)x + (7/-2)

y = 2x - 3.5

The slope of this line is 2. A perpendicular line is found by taking the negative inverse of the slope, which would make this (-1/2). Thus, a perpendicular line would have the form y = -(1/2)x + b. We don't know the value of b since no data are provided to help determine it. The question asks for ANY line that is perpendicular, so all we need to find is an equation with slope of -1/2.

We need to rewrite all the possible answers in standard form to be able to see the slope.

1. 2x + y = 4

y = -2x + 4

2. -4y + 2x = 3

y = (-2/-4)x + 3, or y = (1/2)x + 3

3. -6y = 3x - 24

y = (3/-6)x - 24, or

y = -(1/2)x - 24

4. x + y = -1

y = -x - 1

The only equation with slope -(1/2) is the third, so it is perpendicular to the original line. (Green line below)

Bob

Answer 3

1 looks right.

you want a line with a negative inverse slope

solve each equation for y and the coefficient of the x term is the slope

given equation has slope 2, you want -1/2, which fits the first choice.

2nd choice would have worked, but it has the sign wrong.