What is the slope of the line that passes through the points (6,4) and (3,8)?

2 Answers
Jun 11, 2018

The slope would be -4/3

Explanation:

Another way of thinking of slope is the phrase "rise over run", or:

"rise"/"run"

If you think of a Cartesian graph (all squares!), we can think of the "rise" as the change in the y-axis vs the "run" or change in the x-axis:

"rise"/"run"=(Deltay)/(Deltax)

In this instance, the triangle, Delta (Greek letter delta) means the relative change.

We can calculate the slope of a line using two points, because we can get the relative change in x and y by taking the difference:

(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)

If we say the first coordinate is (3,8), and the second is (6,4), we can calculate the slope:

(y_2-y_1)/(x_2-x_1)

x_1=3
y_1=8

x_2=6
y_2=4

(4-8)/(6-3)

(-4)/3=color(green)(-4/3)

Jun 11, 2018

-4/3

Explanation:

To find the slope, we use: m=(y_2-y_1)/(x_2-x_1).
It honestly does not matter which coordinate is used as 1 or 2 as long as there is consistency.

Now let’s plug in both coordinates into the equation and solve:

m = (4-8)/(6-3)

m = -4/3

Hope this helps!