Question

12 numeric 1 point find the slope of the line between the two points. a(2, 13) and b(10, 7). round your answer to the nearest hundredth (2 decimal places) answer 13 multiple choice 1 point which equation represents the graph (image of a graph) \\( f(x) = |x| + 3 \\) \\( f(x) = |x - 3| \\) \\( f(x) = |x| - 3 \\) \\( f(x) = |x + 3| \\) 14 numeric 1 point simplify \\( 7(2)^6 \\) answer

Explanation:

Step1: Recall slope formula

The slope $m$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Substitute point values

For $A(2,13)$ and $B(10,7)$:
$m=\frac{7-13}{10-2}=\frac{-6}{8}$

Step3: Simplify and round

$\frac{-6}{8}=-0.75$
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Step4: Analyze absolute value graph

The vertex of $f(x)=|x-h|+k$ is $(h,k)$. The graph has vertex $(3,0)$, so $h=3, k=0$.

Step5: Match to equation

Substitute into the form: $f(x)=|x-3|$
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Step6: Calculate exponent first

$2^6=64$

Step7: Multiply by coefficient

$7\times64=448$

Answer:

1. $-0.75$
2. B. $f(x) = |x - 3|$
3. $448$