How do you find the slope given y=2/3x-8?

2 Answers
Tony B
Feb 10, 2016

2/3

Explanation:

The slope (gradient) is the number in front of #x#.

As the 'coefficient' of #x" is "2/3" " #then this is the slope (gradient).

Gió
Feb 10, 2016

I found: slope#=2/3#

Explanation:

Here the equation is in a particularly "friendly" form, with respect to the slope #m#, it is in Slope-Intercept form #y=mx+c#.
The slope can be read directly from your equation as #m=2/3#.
If you want to test it you can consider that the slope is a number that gives you how much #y# changes with a change in #x#.
It seems difficult but you need only to choose two values of #x# say:
#x_1=3#
#x_2=9#
and evaluate the corresponding #y# values:
#y_1=2/3*3-8=-6#
#y_2=2/3*9-8=-2#
and then find the slope as:
#m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)=(-2-(-6))/(9-3)=4/6=2/3#

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