Question

unit 4
lesson 7 homework period
the function $f(x)=\frac{2}{3}x - 8$ is shown on the coordinate grid.

1. use the graph to find the solution $f(x)=-2$. label the point that represents the solution.
2. solve $\frac{2}{3}x - 8=-2$. show your work.
3. use the graph to find the solution $f(x)=-12$. label the point that represents the solution.
4. solve $\frac{2}{3}x - 8=-12$. show your work.

Explanation:

Step1: Solve $f(x)=-2$ graphically

Locate $y=-2$ on the grid, find the corresponding $x$-value on the line: $x=9$. The point is $(9, -2)$.

Step2: Solve $\frac{2}{3}x - 8 = -2$ algebraically

Add 8 to both sides:
$\frac{2}{3}x - 8 + 8 = -2 + 8$
$\frac{2}{3}x = 6$
Multiply by $\frac{3}{2}$:
$x = 6 \times \frac{3}{2}$
$x = 9$

Step3: Solve $f(x)=-12$ graphically

Locate $y=-12$ on the grid, find the corresponding $x$-value on the line: $x=-6$. The point is $(-6, -12)$.

Step4: Solve $\frac{2}{3}x - 8 = -12$ algebraically

Add 8 to both sides:
$\frac{2}{3}x - 8 + 8 = -12 + 8$
$\frac{2}{3}x = -4$
Multiply by $\frac{3}{2}$:
$x = -4 \times \frac{3}{2}$
$x = -6$

Answer:

1. The solution point is $(9, -2)$
2. $x = 9$
3. The solution point is $(-6, -12)$
4. $x = -6$