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

Explanation:

Step1: Identify first line's y-intercept

The purple line crosses the y-axis at $(0, 4)$, so $b_1 = 4$.

Step2: Calculate first line's slope

Use points $(0,4)$ and $(8,1)$: $m_1 = \frac{1-4}{8-0} = \frac{-3}{8}$

Step3: Write first line's equation

Slope-intercept form: $y = mx + b$ $y = -\frac{3}{8}x + 4$

Step4: Identify second line's y-intercept

The green line crosses the y-axis at $(0, -4)$, so $b_2 = -4$.

Step5: Calculate second line's slope

Use points $(0,-4)$ and $(-1,1)$: $m_2 = \frac{1-(-4)}{-1-0} = \frac{5}{-1} = -5$

Step6: Write second line's equation

Slope-intercept form: $y = mx + b$ $y = -5x - 4$

Answer:

$y = -\frac{3}{8}x + 4$ $y = -5x - 4$