Question

find the slope of the line through each pair of points.

1. (-4, 9), (7, -1)
2. (-8, 8), (-4, -14)

solve each equation.

1. 1 - a = 21
2. -16 = 1 + k
3. \\(\frac{n}{9}\\) = 20
4. 14n = 168

Explanation:

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For Question 15:

Step1: Recall slope formula

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(-4,9)$, $(x_2,y_2)=(7,-1)$

Step2: Substitute values into formula

$m=\frac{-1-9}{7-(-4)}=\frac{-10}{11}$

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For Question 16:

Step1: Recall slope formula

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(-8,8)$, $(x_2,y_2)=(-4,-14)$

Step2: Substitute values into formula

$m=\frac{-14-8}{-4-(-8)}=\frac{-22}{4}=-\frac{11}{2}$

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For Question 17:

Step1: Isolate $a$ (subtract 1)

$1 - a - 1 = 21 - 1$
$-a=20$

Step2: Solve for $a$ (multiply by -1)

$a=-20$

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For Question 18:

Step1: Isolate $k$ (subtract 1)

$-16 - 1 = 1 + k - 1$
$k=-17$

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For Question 19:

Step1: Isolate $n$ (multiply by 9)

$\frac{n}{9} \times 9 = 20 \times 9$
$n=180$

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For Question 20:

Step1: Isolate $n$ (divide by 14)

$\frac{14n}{14}=\frac{168}{14}$
$n=12$

Answer:

1. $m=-\frac{10}{11}$
2. $m=-\frac{11}{2}$
3. $a=-20$
4. $k=-17$
5. $n=180$
6. $n=12$