To solve this problem based on the image you provided, let’s break it down step-by-step:

1. Determine the equations for the lines (Line A and Line B)

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

Line A:

• The graph shows Line A passes through points $(0, 12)$ and $(4, 0)$.
• Find the slope ($m$): $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 12}{4 - 0} = \frac{-12}{4} = -3$
• The y-intercept ($b$) is 12 (from the graph, where $x = 0$).
• Equation for Line A: $y = -3x + 12$

Line B:

• The graph shows Line B passes through points $(0, 0)$ and $(3, 12)$.
• Find the slope ($m$): $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 0}{3 - 0} = \frac{12}{3} = 4$
• The y-intercept ($b$) is 0 (from the graph, where $x = 0$).
• Equation for Line B: $y = 4x$

2. Solve the system of equations

To find the solution, solve for the intersection of these two lines: $\text{Line A: } y = -3x + 12$ $\text{Line B: } y = 4x$

Set the two equations equal to each other: $-3x + 12 = 4x$ Solve for $x$: $12 = 7x \implies x = \frac{12}{7}$

Substitute $x = \frac{12}{7}$ into $y = 4x$ to find $y$: