Question

What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)?
The equation of the line in slope-intercept form is y = x

Answer 1

y- intercept = 20

y = $\frac{3}{5}$x + 10 has slope m = $\frac{3}{5}$

The perpendicular slope = -$\frac{1}{m}$ = - $\frac{1}{\frac{3}{5} }$ = -$\frac{5}{3}$

perpendicular equation is y = -$\frac{5}{3}$ x + c

where c is the y-intercept

to find c substitute (15 , -5) into the equation

-5 = - 25 + c ⇒ c = - 5 + 25 = 20

y-intercept of perpendicular line is 20