Slope

1. The slope of the line is $2$.

To measure slope, we pick any two points on the line. Then we look at the horizontal and vertical distances between those points.

Going from the point on the left to the point on the right, the change in $y$ is $2$, and the change in $x$ is $1$.

$\begin{aligned} \text { Slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x} &=\frac{2}{1} \\ &=2 \end{aligned}$

The slope of the line is $2$.

2. The slope of the line is $- \frac {4}{5}$.

To measure slope, we pick any two points on the line. Then we look at the horizontal and vertical distances between those points.

Going from the point on the left to the point on the right, the change in $y$ is $-4$, and the change in $x$ is $5$.

$\begin{aligned} \text { Slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x} &=\frac{-4}{5} \\ &=-\frac{4}{5} \end{aligned}$

The slope of the line is $- \frac {4}{5}$.

3. The slope of the line is $-1$.

To measure slope, we pick any two points on the line. Then we look at the horizontal and vertical distances between those points.

Going from the point on the left to the point on the right, the change in $y$ is $-1$ and the change in $x$ is $1$.

$\begin{aligned} \text { Slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x} &=\frac{-1}{1} \\ &=-1 \end{aligned}$

The slope of the line is $-1$

4. The slope of the line is $\frac {3}{2}$.

To measure slope, we pick any two points on the line. Then we look at the horizontal and vertical distances between those points.

Going from the point on the left to the point on the right, the change in $y$ is $3$, and the change in $x$ is $2$.

$\text { Slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x}=\frac{3}{2}$

The slope of the line is $\frac {3}{2}$.

1. Graph a line that contains the point $(4, 3)$ and has a slope of $\frac {1}{2}$.

2. Graph a line with a slope of $-\frac{2}{5}$ that contains the point $(-3, 5)$.

3. Graph a line with a slope of $4$ that contains the point $(3, 0)$.

4. Graph a line that contains the point $(-2, 7)$ and has a slope of $4$.

1.

Graphing the first point

To graph a line, we need to find two points that are on it. Then we can drag the movable points to those points.

We already have one point, $(4, 3)$, and we can use the slope of the line to find another point.

We want the slope to be $\frac {1}{2}$. Let's look at this slope as a fraction to help us graph the line:

$\text { slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x}=\frac{1}{2}$

Starting at $(4, 3)$, let's go $1$ unit up and $2$ units to the right to plot another point on the line:

The answer

2.

Graphing the first point

To graph a line, we need to find two points that are on it. Then we can drag the movable points to those points.

We already have one point, $(-3, 5)$, and we can use the slope of the line to find another point.

Use the slope to graph another point

We want the slope to be $-\frac {2}{5}$. Let's look at this slope as a fraction to help us graph the line:

$\text { slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x}=\frac{-2}{5}$

Starting at $(-3, 5 )$, let's go 2 units down and 5 units to the right to plot another point on the line:

The answer

3.

Graphing the first point

To graph a line, we need to find two points that are on it. Then we can drag the movable points to those points.

We already have one point, $(3, 0)$, and we can use the slope of the line to find another point.

Use the slope to graph another point

We want the slope to be $4$. Let's look at this slope as a fraction to help us graph the line:

$\text { slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x}=\frac{4}{1}$

Starting at $(3, 0)$, let's go 4 units up and 1 unit to the right to plot another point on the line:

The answer

4.

Graphing the first point

To graph a line, we need to find two points that are on it. Then we can drag the movable points to those points.

We already have one point, $(-2, 7)$, and we can use the slope of the line to find another point.

Use the slope to graph another point

We want the slope to be $4$:

$\text { slope }=\frac{\text { rise }}{\text { run }}=\frac{\Delta y}{\Delta x}=\frac{4}{1}=\frac{-4}{-1}$

Starting at $(-2, 7)$, we don't have room on the given grid to go $4$ units up and $1$ unit right. So let's go $4$ units down and $1$ unit to the left to plot another point on the line.

The answer

1. What is the slope of the line that contains these points?

2. What is the slope of the line that contains these points?

3. What is the slope of the line that contains these points?

4. What is the slope of the line that contains these points?

1. The slope is $-1$.

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

We can calculate the change in $x$ and change in $y$ by picking any two pairs of corresponding $x$- and $y$-values.

So the slope is:

$\frac{\text { Change in } y}{\text { Change in } x}=\frac{-1}{1}=-1$

The slope is $-1$.

2. The slope is $7$.

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

We can calculate the change in $x$ and change in $y$ by picking any two pairs of corresponding $x$- and $y$-values.

So the slope is:

$\frac{\text { Change in } y}{\text { Change in } x}=\frac{21}{3}=7$

The slope is $7$.

3. The slope is $3$.

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

We can calculate the change in $x$ and change in $y$ by picking any two pairs of corresponding $x$- and $y$-values.

So the slope is:

$\frac{\text { Change in } y}{\text { Change in } x}=\frac{3}{1}=3$

The slope is $3$.

4. The slope is $-\frac {2}{5}$

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

We can calculate the change in $x$ and change in $y$ by picking any two pairs of corresponding $x$- and $y$-values.

So the slope is:

$\frac{\text { Change in } y}{\text { Change in } x}=\frac{-2}{5}=-\frac{2}{5}$

The slope is $-\frac {2}{5}$.

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

Choose 1 answer:

A. $\frac {1}{3}$

B. $3$

C. $-3$

D. $-\frac{1}{3}$

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

Choose 1 answer:

A. $\frac {1}{4}$

B. $4$

C. $-\frac{1}{4}$

D. $-4$

3. What is the slope of the line through $(-9,6)$ and $(-3, 9)$?

Choose 1 answer:

A. $\frac {1}{2}$

B. $-2$

C. $-\frac{1}{2}$

D. $2$

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

Choose 1 answer:

A. $- \frac {7}{5}$

B. $- \frac {5}{7}$

C. $\frac {7}{5}$

D. $\frac {5}{7}$

1. C. $-3$.

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

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

The slope is $-3$.

2. B. $4$

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

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

The slope is $4$.

3. A. $\frac {1}{2}$

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

$\begin{aligned} \text { Slope } &=\frac{9-6}{-3-(-9)} \\ &=\frac{3}{6} \\ &=\frac{1}{2} \end{aligned}$

The slope is $\frac {1}{2}$.

4. B. $- \frac {5}{7}$

$\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}$

$\begin{aligned} \text { Slope } &=\frac{-3-2}{3-(-4)} \\ &=\frac{-5}{7} \\ &=-\frac{5}{7} \end{aligned}$

The slope is $-\frac {5}{7}$.