How do you find the slope and intercept of #y=2/3(2x-4)#?

1 Answer
Jan 9, 2016

Answer:

Expand the bracket and then compare to the general equation for a straight line, #y=mx+c#.

Explanation:

The equation shown describes a straight line. For any straight line, we can write an equation with the form:

#y=mx+c#

What does this mean? The letters #y# and #x# are the variables, as usual. The letter #m# refers to the slope of the line - how steep it is. If this number is positive, the line slopes up to the right. If it's negative, the line slopes down. Finally, the letter #c# tells us where the line crosses the #y#-axis. It is called the #y#-intercept.

Let's look more closely at the equation provided.

#y=2/3(2x-4)#

Here we have a bracket containing two terms (#2x# and #-4#), which is all multiplied by #2/3#. This is not in the #mx+c# form that we want! So let's expand the bracket and see what we get:

#y=2/3*2x-2/3*4#
#y=(4x)/3-8/3#

Now compare this to the general equation for a straight line, #y=mx+c#. You can see that #m=4/3# since that's what the #x# is being multiplied by. The term without #x# in it is our #y#-intercept, #c#.

#m=4/3#
#c=-8/3#

We conclude that the slope of this line is #4# in #3#. It crosses the #y#-axis at a height of #-8/3#, or #-2.6# recurring.