Question

write an equation in slope - intercept form of a line that passes through the point (5,3) and is perpendicular to the line represented by $y = -\frac{1}{4}x + 3$.

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line is $m_1 =-\frac{1}{4}$. For two perpendicular lines, the product of their slopes is - 1. Let the slope of the required line be $m_2$. Then $m_1\times m_2=-1$. So, $-\frac{1}{4}\times m_2 = - 1$, and $m_2 = 4$.

Step2: Use the point - slope form to find the equation

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(5,3)$ and $m = 4$. Substitute these values: $y - 3=4(x - 5)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-3 = 4x-20$. Add 3 to both sides of the equation: $y=4x-17$.

Answer:

$y = 4x-17$