Question

Line EF has an equation of a line y = −2x + 7. Which of the following could be an equation for a line that is perpendicular to line EF?

y = 2x − 3
y = 1 over 2x − 3
y = −2x − 3
y = −1 over 2x − 3

Answer 1

1.

When a line is given in the form y=mx+n,

m is the slope of this line.

For example, the slope of the line y=-2x+7 is -2.

2.

If lines y=mx+n and y=kx+t are perpendicular, then the multiplication of their slopes is -1, that is

m*k = -1, so k=-1/m

3.

any line perpendicular to y=-2x+7 has slope = -1/(-2)=1/2

4.

Among the choices, y=(1/2)x-3 is a line perpendicular to the given line.

Answer:

b. y=(1/2)x-3

Answer 2

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

Explanation:

Step 1

Find the slope of the line EF

we have

`y=-2x+7`

The slope of the line EF is equal to

`m=-2`

Step 2

Find the slope of the line perpendicular to the line EF

we know that

If two lines are perpendicular, then the product of its slopes is equal to minus one

so

`m1*m2=-1`

we have

`m1=-2` -----> slope of the line EF

Find the value of m2

substitute

`(-2)*m2=-1`

`m2=1/2`

therefore

the equation
`y=(1)/(2) x-3` could be an equation for a line that is perpendicular to line EF