sylvie finds the solution to the system of equations by graphing.\ny = \\frac{2}{3}x + 1 and y =…

Explanation:

Step1: Identify slope - intercept form

The equations are in slope - intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $y=\frac{2}{3}x + 1$, the slope $m_1=\frac{2}{3}$ and y - intercept $b_1 = 1$. For $y=-\frac{2}{3}x - 1$, the slope $m_2=-\frac{2}{3}$ and y - intercept $b_2=-1$.

Step2: Analyze y - intercepts

The line $y=\frac{2}{3}x + 1$ crosses the y - axis at the point $(0,1)$ and the line $y=-\frac{2}{3}x - 1$ crosses the y - axis at the point $(0, - 1)$.

Step3: Analyze slopes

The line $y=\frac{2}{3}x + 1$ has a positive slope, so it rises from left to right. The line $y=-\frac{2}{3}x - 1$ has a negative slope, so it falls from left to right.

Answer:

The graph where one line crosses the y - axis at $(0,1)$ and rises with a slope of $\frac{2}{3}$ and the other line crosses the y - axis at $(0, - 1)$ and falls with a slope of $-\frac{2}{3}$. (Since no option identifiers are given, a description of the correct graph is provided).