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 of blue line

The blue line has a y - intercept $b = 3$. Using two points $(-6,0)$ and $(0,3)$ to find the slope $m=\frac{3 - 0}{0-(-6)}=\frac{1}{2}$. So the equation is $y=\frac{1}{2}x + 3$.

Step3: Find equation of green line

The green line has a y - intercept $b = 6$. Using two points $(0,6)$ and $(8,0)$ to find the slope $m=\frac{0 - 6}{8 - 0}=-\frac{3}{4}$. So the equation is $y=-\frac{3}{4}x+6$.

Answer:

$y=\frac{1}{2}x + 3$ $y=-\frac{3}{4}x+6$