Question

Give the equation of a line that goes through the point ( − 21 , 2 ) and is perpendicular to the line 7 x − 4 y = − 12 . Give your answer in slope intercept form

Answer 1

Given:

Equation of line
`7x-4y=-12`.

To find:

The equation of line that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.

Solution:

The given equation of line can be written as

`7x-4y+12=0`

Slope of line is

`\text{Slope}=-\frac{\text{Coefficient of x}}{\text{Coefficient of y}}`

`m_1=-(7)/((-4))`

`m_1=(7)/(4)`

Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is

`m_1m_2=-1`

`m_2=-(1)/(m_1)`

`m_2=-(4)/(7)`
`[\because m_1=(7)/(4)]`

Now, the slope of perpendicular line is
`m_2=(4)/(7)` and it goes through (-21,2). So, the equation of line is

`y-y_1=m_2(x-x_1)`

`y-2=-(4)/(7)(x-(-21))`

`y-2=-(4)/(7)x-(4)/(7)(21)`

`y-2=-(4)/(7)x-12`

`y=-(4)/(7)x-12+2`

`y=-(4)/(7)x-10`

Therefore, the required equation in slope intercept form is
`y=-(4)/(7)x-10`.