Question

write an equation in slope - intercept form for each graph shown.
3)
graph with points (0, -5) and (4, -2)
4)
graph with points (0, 2) and (2, -4)

Explanation:

Step1: Analyze Graph 3

We have two points \((0, -5)\) and \((4, -2)\). The slope-intercept form is \(y = mx + b\), where \(b\) is the y-intercept. From \((0, -5)\), \(b = -5\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - (-5)}{4 - 0}=\frac{3}{4}\). So the equation is \(y=\frac{3}{4}x - 5\).

Step2: Analyze Graph 4

We have two points \((0, 2)\) and \((2, -4)\). The y-intercept \(b = 2\) from \((0, 2)\). The slope \(m=\frac{-4 - 2}{2 - 0}=\frac{-6}{2}=-3\). So the equation is \(y=-3x + 2\).

Answer:

For Graph 3: \(y=\frac{3}{4}x - 5\)
For Graph 4: \(y=-3x + 2\)