Find an equation for the line perpendicular Write your answer in the form y = m x + b?

Slope of the line (3x + 15y = 90)
= -3/15
= -1/5

When two lines are perpendicular, the product of their slopes = -1
Slope of the required line, m,
= -1 / (-1/5)
= 5

Then, equation of the required line is y = 5x + b

The line passes through (7, - 8). Substitute x = 7 and y = -8 into the line y = 5x + b :
-8 = 5(7) + b
b = -43

Hence, the equation of the required line : y = 5x - 43

3x + 15y = 90 ← this is the line (ℓ1)

15y = - 3x - 90 → you can simplify by 3

5y = - x - 30

y = (- x - 30)/5

y = - (1/5).x - (30/5)

y = - (1/5).x - 6 ← the slope is (- 1/5)


The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept

Two lines are perpendicular if the product of their slope is - 1.

As the slope of the line (ℓ1) is (- 1/5), the slope of the line (ℓ2) is (5).

The equation of the line (ℓ2) becomes: y = 5x + b

The line (ℓ2) passes through M (7 ; - 8), so the coordinates of this point must verify the equation of the line (ℓ2).

y = 5x + b

b = y - 5x → you substitute x and y by the coordinates of the point M (7 ; - 8)

b = - 8 - (5 * 7) = - 8 - 35 = - 43


→ The equation of the line (ℓ2) is: y = 5x - 43