Question

1. given $f(x) = \frac{3}{4}x - 6$

find $f(8) = $
find $x$ so that $f(x) = 18$

1. given $h(x) = \frac{2}{3}x - 4$ fill in the table.

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$$\begin{tabular}{|c|c|} \\hline $x$ & $h(x)$ \\\\ \\hline 12 & \\\\ \\hline -3 & \\\\ \\hline & 24 \\\\ \\hline \\end{tabular}$$

1. solve for $y$ then state the slope of the line. $4x - 3y = 15$

$m = $

Explanation:

Step1: Substitute x=8 into f(x)

$f(8) = \frac{3}{4}(8) - 6$

Step2: Calculate f(8)

$f(8) = 6 - 6 = 0$

Step3: Set f(x)=18, solve for x

$\frac{3}{4}x - 6 = 18$

Step4: Isolate the x-term

$\frac{3}{4}x = 18 + 6 = 24$

Step5: Solve for x

$x = 24 \times \frac{4}{3} = 32$

Step6: Substitute x=12 into h(x)

$h(12) = \frac{2}{3}(12) - 4$

Step7: Calculate h(12)

$h(12) = 8 - 4 = 4$

Step8: Substitute x=-3 into h(x)

$h(-3) = \frac{2}{3}(-3) - 4$

Step9: Calculate h(-3)

$h(-3) = -2 - 4 = -6$

Step10: Set h(x)=24, solve for x

$\frac{2}{3}x - 4 = 24$

Step11: Isolate the x-term

$\frac{2}{3}x = 24 + 4 = 28$

Step12: Solve for x

$x = 28 \times \frac{3}{2} = 42$

Step13: Rearrange 4x-3y=15 to solve for y

$-3y = -4x + 15$

Step14: Solve for y

$y = \frac{4}{3}x - 5$

Step15: Identify slope from y=mx+b

Slope $m = \frac{4}{3}$

Answer:

1. $f(8) = 0$
2. $x = 32$
3. For $h(x)$ table:

• When $x=12$, $h(x)=4$
• When $x=-3$, $h(x)=-6$
• When $h(x)=24$, $x=42$

1. Solved for $y$: $y = \frac{4}{3}x - 5$; Slope $m = \frac{4}{3}$