Equation of a line that has $y$-intercept 5 and is perpendicular to the line joining $(2,-3)$ and $(

Question

Equation of a line that has $y$-intercept 5 and is perpendicular to the line joining $(2,-3)$ and $(4,2)$ is

Professor PC Thomas Classes · Answer

Slope of given line $m_1 = \frac{2 - (-3)}{4 - 2} = \frac{5}{2}$. Slope of perpendicular line $m_2 = -\frac{2}{5}$. Equation: $y = mx + c \implies y = -\frac{2}{5}x + 5 \implies 5y = -2x + 25 \implies 2x + 5y - 25 = 0$.