Question

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

Answer 1

`"slope "=1/8`

Explanation:

`"to calculate the slope m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-9,1)" and "(x_2,y_2)=(7,3)`

`rArrm=(3-1)/(7-(-9))=2/16=1/8`

Answer 2

The slope of the line segment AB is `0.125`

Explanation:

`" "`
Slope is basically how steep a line is.

A slope is often denoted by the variable `color(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.

`color(green)("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:

`color(green)("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, `Rise = "2 Units"`.

It moves to the right `"16 Units"` and reach the Point B(7,3).

Hence, `"Run = 16 Units"`.

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

`color(green)("Step 3")`

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

Hence,

`Slope (m) = 2/16`

`Slope (m) = cancel 2^color(red)(1)/cancel 16^color(red)8`

`m=1/8`

`m=0.125`

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