Interpreting Slope as a Rate of Change Practice

1. What is the slope of the line through $(-10,1)$ and $(0,-4)$?
   

   Choose 1 answer:
   

   1. $2$

   2. $\dfrac{1}2$

   3. $-\dfrac{1}2$

   4. $-2$

2. What is the slope of the line through $(-1,8)$ and $(3,-4)$?

   Choose 1 answer:
   

   1. $-\dfrac{1}3$

   2. $-3$

   3. $\dfrac{1}3$

   4. $3$

3. What is the slope of the line through $(-7,-8)$ and $(0,4)$?

   Choose 1 answer:
   

   1. $\dfrac{12}7$

   2. $-\dfrac{7}{12}$

   3. $-\dfrac{12}7$

   4. $\dfrac{7}{12}$

4. What is the slope of the line through $(-1,-7)$ and $(3,9)$?

   Choose 1 answer:
   

   1. $\dfrac{1}4$

   2. $4$

   3. $-\dfrac{1}4$

   4. $-4$

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/e/slope-from-two-points
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1. $\text{Slope}=\dfrac{\text{Rise}}{\text{Run}}=\dfrac{\text{Change in }y}{\text{Change in }x}$

   $\begin{aligned}\text{Slope}&=\dfrac{-4-1}{0-(-10)}\\\\&=\dfrac{-5}{10}\\\\&=-\dfrac{1}{2}\end{aligned}$

   The slope is $-\dfrac{1}{2}$.

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2. $\text{Slope}=\dfrac{\text{Rise}}{\text{Run}}=\dfrac{\text{Change in }y}{\text{Change in }x}$

   $\begin{aligned}\text{Slope}&=\dfrac{-4-8}{3-(-1)}\\\\&=\dfrac{-12}{4}\\\\&=-3\end{aligned}$

   The slope is $-3$.

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3. $\text{Slope}=\dfrac{\text{Rise}}{\text{Run}}=\dfrac{\text{Change in }y}{\text{Change in }x}$

   $\begin{aligned}\text{Slope}&=\dfrac{4-(-8)}{0-(-7)}\\\\&=\dfrac{12}{7}\end{aligned}$

   The slope is $\dfrac{12}{7}$.

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4. $\text{Slope}=\dfrac{\text{Rise}}{\text{Run}}=\dfrac{\text{Change in }y}{\text{Change in }x}$

   $\begin{aligned}\text{Slope}&=\dfrac{9-(-7)}{3-(-1)}\\\\&=\dfrac{16}{4}\\\\&=4\end{aligned}$

   The slope is $4$.
   

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