For this problem, we are given a certain system of equations and we need to identify the slope, y-intercept and trace the graphs for the system.
The system is given below:
[tex]\begin{cases}y={-\frac{2x}{7}}+2 \\ y=-{\frac{5x}{6}}-18\end{cases}[/tex]Both equations are in the slope-intercept form, which means that the slope is the number multiplying "x" and the intercept is the number isolated.
For equation 1:
[tex]\begin{gathered} \text{ slope}=\frac{-2}{7}\\ \\ \text{ intercept}=2 \\ \end{gathered}[/tex]For equation 2:
[tex]\begin{gathered} \text{ slope}=\frac{-5}{6} \\ \text{ intercept}=-18 \end{gathered}[/tex]The slope is the increase on the graph that the y-axis has for each 1 unit increase in the x-axis. This means that from x = 0 to x = 1 the first equation will decrease 2/7 units and the second equation will decrease 5/6 units. The y-intercept is the point at which the function crosses the y-axis.
With this we can create the graphs:
