Question

What is the equation of the line that is perpendicular to the line y=3/5xplus 10 and passes through the point (15,-5)?

Answer 1

Step-by-step explanation:

a general line equation is

y = ax + b

the original line is

y = 3/5 x + 10

the factor of x is always the slope (inclination of the line).

it is "y change/x change".

the slope of a perpendicular line (angle of 90°) is turning the slope of the original line upside-down and flips the sign.

so, it is -5/3.

we use the point information to get the right "b" for our new line :

-5 = -5/3 × 15 + b

-5 = -5×5 + b

-5 = -25 + b

b = 20

so, the perpendicular line equation going through (15, -5) is

y = -5/3 x + 20