Question

 Find the equation of the line that is perpendicular to 4 x + 3 y = 5 and goes through the point (3, –3)

Answer 1

Step-by-step explanation:

the line equation

y = ax + b

gives us slope (a) and y-interception (b).

4x + 3y = 5

3y = -4x + 5

y = -4/3 × x + 5/3

the slope of the original line is therefore -4/3.

a perpendicular slope flips x and y upside-down and flips the sign.

so, the perpendicular slope of -4/3 is 3/4.

the desired line looks like

y = 3/4 × x + b

b we get by using the given point and its coordinates :

-3 = 3/4 × 3 + b = 9/4 + b

-12/4 = 9/4 + b

b = -21/4

so our full line equation is

y = 3/4 × x - 21/4

or

4y = 3x - 21

-3x + 4y = -21