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

2 Answers
Ben
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)#

Isabella
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!

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