Question

What is the equation for​

Answer 1

The equation of a line that is perpendicular to the given line is y = –4x – 16.

Solution:

The equation of a line given is y = 0.25x – 7

Slope of the given line(
`m_1`) = 0.25

Let
`m_2` be the slope of the perpendicular line.

Passes through the point (–6, 8).

If two lines are perpendicular then the product of the slopes equal to –1.

`\Rightarrow m_1 \cdot m_2=-1`

`\Rightarrow 0.25\cdot m_2=-1`

`\Rightarrow m_2=(-1)/(0.25)`

`\Rightarrow m_2=-4`

Point-slope intercept formula:

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

`x_1=-6, y_1=8` and
`m=-4`

Substitute these in the formula, we get

`y-8=-4(x-(-6))`

`y-8=-4(x+6)`

`y-8=-4x-24`

Add 8 on both sides of the equation.

`y-8+8=-4x-24+8`

`y=-4x-16`

Hence the equation of a line that is perpendicular to the given line is

y = –4x – 16