Question

22 what is the equation of the line that passes through point a and is perpendicular to line c? write your answer in slope intercept form. y = \square x + \square

Explanation:

Step1: Find slope of Line C

Line C passes through \((0, 6)\) and \((6, 0)\). Slope \(m_C=\frac{0 - 6}{6 - 0}=\frac{-6}{6}=-1\).

Step2: Find slope of perpendicular line

Perpendicular slope \(m\) satisfies \(m\times m_C=-1\). So \(m\times(-1)=-1\Rightarrow m = 1\).

Step3: Identify Point A's coordinates

From graph, Point A is \((-4, -3)\).

Step4: Use point - slope form \(y - y_1=m(x - x_1)\)

Substitute \(m = 1\), \(x_1=-4\), \(y_1=-3\):
\(y-(-3)=1\times(x - (-4))\Rightarrow y + 3=x + 4\).

Step5: Convert to slope - intercept form (\(y=mx + b\))

Subtract 3 from both sides: \(y=x + 4-3\Rightarrow y=x + 1\).

Answer:

\(y = 1x+1\) (or \(y=x + 1\))