what system of equations does the graph show? write the equations in slope - intercept form. simplify any…

Explanation:

Step1: Find slope - intercept form formula

The slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find equation for red line

The red line has a y - intercept ($b$) of 7. Using two points $(0,7)$ and $(1,0)$ to find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 7}{1 - 0}=-7$. So the equation is $y=-7x + 7$.

Step3: Find equation for purple line

The purple line has a y - intercept ($b$) of - 6. Using two points $(0,-6)$ and $(6,-4)$ to find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4+6}{6 - 0}=\frac{1}{3}$. So the equation is $y=\frac{1}{3}x-6$.

Answer:

$y=-7x + 7$ $y=\frac{1}{3}x-6$