Question

write an equation in slope-intercept form of the line shown.
an equation is:

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((-4, 2)\) and \((-2, -2)\):
\( m=\frac{-2 - 2}{-2 - (-4)}=\frac{-4}{2}=-2 \)

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Let's use the point \((-4, 2)\) and \( m = - 2 \):
\( y - 2=-2(x + 4) \)

Step3: Convert to slope - intercept form (\(y=mx + b\))

Expand the right - hand side: \( y - 2=-2x-8 \)
Add 2 to both sides: \( y=-2x - 6 \)

Answer:

\( y=-2x - 6 \)