y-intercept: The Start of Your Line

The y-intercept of a line is nothing more than an ordered pair.  The only special thing about the y-int is that the x-value must be zero.

     Examples:  (0, 5) (0, 3) (0, -4) (0, 18)


Notice the common trend, the first number (x) is always 0.

Finding the y-intercept from an Equation

To find the y-int, plug in x = 0 for your equation, and solve for y.


y = 4x + 3


y = 4(0) + 3

plug in x = 0  

y =  0 + 3


y = 3

solve for y  

(0, 3)

write the point as (0, y)  

Instead of writing the y-int as (0, 3), we can also write it as...

y - intercept = 3, or for short, y-int = 3.


The y-intercept is also often written as b = 3.  We use the letter b to represent the beginning of the line.  We use this to help us graph a line in the coordinate plane.

Finding the y-intercept from a Table of Values

A table of values is a list of ordered pairs written as a table...

x 0 1 2 3 4
y 2 4 6 8 10

We want to find the place where x = 0.  The matching y value right below there is our y-intercept.  Take a look...

y-int = 2

Sometimes the value where x = 0 will not be shown in the table.  In this situation, you will need to continue the pattern until you find x = 0.

x 2 4 6 8 10
y 5 8 11 14 17

Continue the pattern...




I knew that the numbers to the left had to be 0 and 4 because I continued the pattern of adding 2 and adding 3.  The y-int = 4.


Finding the y-intercept from a Graph

The y-int from a graph is still the y value where x = 0.  Luckily, there is a really easy way to find it.  Just look for the place where your line crosses the y-axis.

Look for yellow and blue lines to make a green dot...

The y-int is the green dot shown above.  The x-value is 0, and the y-value is 1.  That is why the point is (0, 1).

The y-intercept is often paired with slope.  Learn how to graph using the slope and y-intercept or take a look at slope intercept form.

Return to more free algebra help topics.




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