The equation of the line is:
[tex]y=-\frac{3}{2}x+3[/tex]This equation is equal to "9" in part (a) and "-3" in part (b).
How do we solve the equation in part(a) and part(b) using graph?
We look at y = 9 and see at which x value it intersects with the graph.
Similarly, we look at y = -3 and see at which x value it intersects with the graph.
a)
We draw a horizontal line at y = 9. The point where it intersects the line drawn, we draw a vertical line to connect to the x-axis. So, it connects at x = -4. This is the solution. Let's check it algebraically as well.
[tex]\begin{gathered} 9=-\frac{3}{2}x+3 \\ \frac{3}{2}x=3-9 \\ \frac{3}{2}x=-6 \\ x=-\frac{6}{\frac{3}{2}} \\ x=-6\times\frac{2}{3} \\ x=-4 \end{gathered}[/tex]b)
We draw a horizontal line at y = -3. The point where it intersects the line drawn, we draw a vertical line to connect to the x-axis. So, it connect at x = 4. Tis is the solution. Let's check algebraically:
[tex]\begin{gathered} -3=-\frac{3}{2}x+3 \\ \frac{3}{2}x=3+3 \\ \frac{3}{2}x=6 \\ x=\frac{6}{\frac{3}{2}} \\ x=6\times\frac{2}{3} \\ x=4 \end{gathered}[/tex]