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

Explanation:

Step1: Identify line 1 (blue) intercepts

The blue line crosses the y-axis at $(0, -1)$ and the x-axis at $(-1, 0)$.

Step2: Calculate slope of line 1

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{-1 - 0} = -1$

Step3: Write line 1 in slope-intercept form

Using $y = mx + b$ where $m=-1$, $b=-1$: $y = -x - 1$

Step4: Identify line 2 (purple) intercepts

The purple line crosses the y-axis at $(0, -7)$ and the x-axis at $(4, 0)$.

Step5: Calculate slope of line 2

Slope $m = \frac{0 - (-7)}{4 - 0} = \frac{7}{4}$

Step6: Write line 2 in slope-intercept form

Using $y = mx + b$ where $m=\frac{7}{4}$, $b=-7$: $y = \frac{7}{4}x - 7$

Answer:

$y = -x - 1$ $y = \frac{7}{4}x - 7$