Find the slope of the line that passes through (-8,11) and (2,-3).

Question

Find the slope of the line that passes through (-8,11) and (2,-3).

Answer 1

Hey there. So the slope of a line can be calculated for two points (-8,11) and (2,-3) as follows.

The slope of a line is always the rise over the run, which translated into points is the difference in the y values over the difference in the x values.

To show an example of this, take the y values in this case, 11 and -3.

The difference is the result of subtracting two values, so the difference here is either

11 - -3 = 11 + 3 = ....

Got it? 14!

Or...

-3 -11 = -14...

So either way, the difference can be 14 or -14 for the y values.

For the x values, -8 and 2, the difference (subtraction) is either -8 - 2 = ...-10 right?

Or, 2 - -8 = 2 + 8 = 10...

So, the slope is the quotient of the two differences.

In this case, the slope can either be 14 or -14 for the y values divided by -10 or 10 for the x values.

Just remember to divide the same way and you will always get the right answer.

In this case, 14 can be divided by -10. That gives -1.4

Or, the other values -14 can be divided by 10, giving -1.4 as well.

You will get the same answer because both are right.

So the slope of the line is either -1.4 or in fraction form, -14/10 simplifies to -7/5.

More information:

To understand the formula for the slope,

(y2 - y1) / (x2 - x1)

The values of (-8,11) (2,3) can be either thought of as (x1, y1) (x2, y2) or the opposite, as we showed above with the two differences, the same result will be obtained if they are switched to -8 being applied to x2 instead, but this is only because the ordering of the points for calculating slope is arbitrary.

By the way, the difference in the y values can be thought of, and is literally equal to, the value of the height difference between the two points, which is called the rise. And the difference in the x values would then be the run, the span of the distance between the points. In this case, we are quite literally dividing rise over run to find the steepness of the slope.

I hope that helps!

Answer 2

(-8, 11) and (2, -3) have a line through them with slope = (11- -3)/(-8-2) = 14/-10 = - 7/5

slope = the difference in y coordinates divided by the difference in x coordinates = "rise over run"