# What is the slope of the line passing through the following points: (-9,1) , (7,3)?

Apr 14, 2018

$\text{slope } = \frac{1}{8}$

#### Explanation:

$\text{to calculate the slope m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-9,1)" and } \left({x}_{2} , {y}_{2}\right) = \left(7 , 3\right)$

$\Rightarrow m = \frac{3 - 1}{7 - \left(- 9\right)} = \frac{2}{16} = \frac{1}{8}$

Apr 14, 2018

The slope of the line segment AB is $0.125$

#### Explanation:

$\text{ }$
Slope is basically how steep a line is.

A slope is often denoted by the variable $\textcolor{red}{m}$.

A slope is Positive when the line is increasing when viewed from the left.

A slope is Negative when the line is decreasing when viewed from the left.

A Zero Slope means the line is neither increasing nor decreasing when viewed from the left.

A Horizontal Line is an example of having a Zero Slope.

An undefined slope is a unique situation:

Consider a Vertical Line.

A vertical line is neither moving to the left nor to the right.

Hence, the slope for a vertical line is undefined.

$\textcolor{g r e e n}{\text{Step 1}}$

To find the SLOPE of the line passing through the Points color(red)((-9,1) and (7, 3), plot the Ordered Pair of points on a Cartesian coordinate system as shown:

$\textcolor{g r e e n}{\text{Step 2}}$

Join the points A and B and obtain a line segment AB.

If you observe the steepness of the line, you see that there is a shallow positive slope.

Find out how many units does it go up (Rise) ?

Next, find out how many units does it go side-to-side (Run)?

Observe in the sketch above, it goes up by 2 units.

Hence, $R i s e = \text{2 Units}$.

It moves to the right $\text{16 Units}$ and reach the Point B(7,3).

Hence, $\text{Run = 16 Units}$.

The next step shows these calculations in on a graph (image).

$\textcolor{g r e e n}{\text{Step 3}}$

Slope (m) can be found by using the ratio color(red)("Rise"/"Run"

Hence,

$S l o p e \left(m\right) = \frac{2}{16}$

$S l o p e \left(m\right) = {\cancel{2}}^{\textcolor{red}{1}} / {\cancel{16}}^{\textcolor{red}{8}}$

$m = \frac{1}{8}$

$m = 0.125$

Hence, the slope of the line segment AB is $0.125$