What is intercept form?

Question

In my book, it converts x+2y=3 into (x)/3 + (2y)/3 =1 

 

I am so confused by this. 

Answer 1

Kyle,

 

Working the problem in a slightly different way, I got the same answer as Paul:

 

Start with the given equation.

 

x + 2y = 3

 

It is good to put it in the form 

 

y = mx + b

 

where m = slope and b = y-intercept.

 

Solving for y,

 

2y = -x + 3

 

y = (-1/2)x + 3/2

 

Them m = -1/2, and b = 3/2.  The y intercept is 3/2, which is the value of y when x = 0.  Similarly, when y = 0, the value of x is 3.  it comes from

 

0 = (-1/2)x + 3/2 ⇒ x = 3

 

If the book says the y intercept is 2/3, then it must be a misprint.

 

Answer 2

The idea behind the intercept form of a line is that it makes it easy to find the values at which the line crosses (or intercepts) the x- and y-axes. In general the intercept form of a line looks like

 

x/a + y/b = 1

 

In this case, the x-intercept of this line is a, and the y-intercept is b. The important part that makes this work is that the constant term (on the right side) is 1. For your line, we can take the equation x + 2y = 3 and divide both sides by 3 (the constant term) to get x/3 + y/(3/2) = 1, telling you that the x-intercept is 3 and the y-intercept is 3/2.