Mathematics: 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

4/6 = x + 3/ 12 - x4( 12 - x) = 6( x + 3)48 - 4x = 6x + 18-4x - 6x = 18 - 48- 10x = -30x = 3...

Give the equation of a line that goes through the

cordobamariana07

02.02.2022

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

0,0(0 оценок)