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

$\text{Slope}=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}$

$m_1=-\dfrac{7}{(-4)}$

$m_1=\dfrac{7}{4}$

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

$m_1m_2=-1$

$m_2=-\dfrac{1}{m_1}$

$m_2=-\dfrac{4}{7}$           $[\because m_1=\dfrac{7}{4}]$

Now, the slope of perpendicular line is $m_2=\dfrac{4}{7}$ and it goes through (-21,2). So, the equation of line is

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

$y-2=-\dfrac{4}{7}(x-(-21))$

$y-2=-\dfrac{4}{7}x-\dfrac{4}{7}(21)$

$y-2=-\dfrac{4}{7}x-12$

$y=-\dfrac{4}{7}x-12+2$

$y=-\dfrac{4}{7}x-10$

Therefore, the required equation in slope intercept form is $y=-\dfrac{4}{7}x-10$.