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

1 Answer
Jan 9, 2016

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.