Question

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ? Enter your answer in the box.

Answer 1

y=-4x+15

Explanation:

Simple Math

Answer 2

`y=-4x+15`

Explanation:

The correct question is

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=(x/4)+5 ?

step 1

Find out the slope of the given line

we have

`y=(1)/(4)x+5`

so

the slope is

`m=(1)/(4)`

step 2

Find out the slope of the line perpendicular to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

`m_1*m_2=-1`

we have

`m_1=(1)/(4)`

substitute

`(1)/(4)*m_2=-1`

`m_2=-4`

step 3

Find the equation of the line

The equation of the line in point slope form is

`y-y_1=m(x-x_1)`

we have

`(x_1,y_1)=(2,7)`

`m=-4`

substitute

`y-7=-4(x-2)`

Convert to slope intercept form

`y=mx+b`

`y-7=-4x+8`

`y=-4x+8+7`

`y=-4x+15`