Question

#10 - 20 find the slope using the two coordinates. *answers in lowest terms.

1. (-1, -1), (3, -3)

slope __________

1. (-6, -12),(-6, 3)

slope __________

1. (8, 3), (-8, 17)

slope __________

Explanation:

Step1: Recall slope formula

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

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For problem 10: $(-1, -1), (3, -3)$

Step1: Assign coordinates

Let $(x_1,y_1)=(-1,-1)$, $(x_2,y_2)=(3,-3)$

Step2: Substitute into slope formula

$m=\frac{-3 - (-1)}{3 - (-1)}=\frac{-3+1}{3+1}=\frac{-2}{4}$

Step3: Simplify fraction

$m=\frac{-1}{2}$

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For problem 11: $(-6, -12),(-6, 3)$

Step1: Assign coordinates

Let $(x_1,y_1)=(-6,-12)$, $(x_2,y_2)=(-6,3)$

Step2: Substitute into slope formula

$m=\frac{3 - (-12)}{-6 - (-6)}=\frac{3+12}{-6+6}=\frac{15}{0}$

Step3: Identify undefined slope

Division by 0 is undefined, so slope is undefined.

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For problem 12: $(8, 3), (-8, 17)$

Step1: Assign coordinates

Let $(x_1,y_1)=(8,3)$, $(x_2,y_2)=(-8,17)$

Step2: Substitute into slope formula

$m=\frac{17 - 3}{-8 - 8}=\frac{14}{-16}$

Step3: Simplify fraction

$m=\frac{-7}{8}$

Answer:

1. $\frac{-1}{2}$
2. Undefined
3. $\frac{-7}{8}$