Question

what is the equation, in point - slope form, of the line that is perpendicular to the given line and passes through the point (-4, -3)?
○ ( y + 3 = -4(x + 4) )
○ ( y + 3 = -\frac{1}{4}(x + 4) )
○ ( y + 3 = \frac{1}{4}(x + 4) )
○ ( y + 3 = 4(x + 4) )
(graph description: coordinate plane with points (-1,1), (-4,-3), (0,-3), and a blue line plotted)

Explanation:

Step1: Find slope of given line

Use points \((-1,1)\) and \((0,-3)\). Slope \(m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - 1}{0 - (-1)}=\frac{-4}{1}=-4\).

Step2: Find slope of perpendicular line

Perpendicular slope \(m_{\perp}=-\frac{1}{m}=-\frac{1}{-4}=\frac{1}{4}\).

Step3: Use point - slope form

Point - slope form: \(y - y_1 = m(x - x_1)\), with \((x_1,y_1)=(-4,-3)\) and \(m=\frac{1}{4}\). Substitute: \(y - (-3)=\frac{1}{4}(x - (-4))\), so \(y + 3=\frac{1}{4}(x + 4)\).

Answer:

\(y + 3=\frac{1}{4}(x + 4)\) (the third option: \(y + 3=\frac{1}{4}(x + 4)\))