The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept
Equation of the line (ℓ1):
y = (3/4)x + 5 → the slope is (3/4)
Two lines are perpendicular if the product of their slope is: - 1
slope_ ℓ1 * slope_ ℓ2 = - 1
slope_ ℓ2 = - 1/slope_ ℓ1 → you know that: slope_1 = (3/4)
slope_ ℓ2 = - 1/(3/4)
slope_ ℓ2 = - 4/3 → so, the slope of the line (ℓ2) is: - 4/3
Recall: the typical equation of a line is: y = mx + b
The equation of the line (ℓ2) becomes: y = - (4/3)x + b
You know that the lines (ℓ2) passes through the point (3 ; 5). So the coordinates of this point must verify the equation of the line (ℓ2) because this point belongs to the line (ℓ2).
y = - (4/3)x + b
b = y + (4/3)x → you substitute x and y by the coordinate of the point
b = 5 + [(4/3) * 3]
b = 5 + 4
b = 9
