Question

what system of equations does the graph show?
write the equations in slope-intercept form. simplify any fractions.
$y =$
$y =$

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:

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