Academic Subjects
Math
Algebra
Linear Equations
Equation Of Line Perpendicular To 2x + 7y + 4

Find the equation of the line that passes through the point (7, -12) and is perpendicular to the line 2x + 7y + 4



First, let's find the slope of this line by rearranging the provided equation
so it will fit the standard form y = mx + b

2x + 7y + 4 = 0

7y = - 2x - 4

y = -
2 / 7
x -
4 / 7



The slope of this equation is -
2 / 7


The slope of the line perpendicular to this one will be the negative invert, i.e.

7 / 2


Finally, we will plug the provided coordinates (7, -12) into y = mx + b

-12 =
7 / 2
(7) + b


now we solve for b

-12 =
49 / 2
+ b

-12 = 24.5 + b

-24.5 - 12 = b

b = - 36.5

The line perpendicular to 2x + 7y + 4 is

y =
7 / 2
x - 36.5

>h3>equation of a line graph of the Line Perpendicular To 2x + 7y + 4