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Finding the YIntercept from a Linear Equation
(KS3, Year 9)
The Lesson
The yintercept is where a line crosses the yaxis.A line can be represented by a linear equation. We can find the yintercept from a linear equation.
Interactive Widget
You can use this interactive widget to create a graph of a linear equation and see its yintercept. Use the buttons to change the values of the linear equation.Real Examples of Finding the YIntercept from a Linear Equation
Finding the yintercept of a line from a linear equation is easy. Here are some linear equations, which represent lines. We show how to find the yintercept from the linear equation.
The yintercept of y = 2x + 1 is 1.
Look at the constant term (the one that does not contain the variables x or y). This is the yintercept. 
The yintercept of y = −3x + 3 is 3.

The yintercept of y = x − 2 is −2.
Look at the sign in front of the constant. If it is a minus sign (−) the yintercept must also have a minus sign. The yintercept is negative; it is below the xaxis. 
The yintercept of y = 4x is 0.
There is no constant term. The yintercept is 0.
Understanding Finding the YIntercept from a Linear Equation
A linear equation (in slopeintercept form) is given in the form below:To find the yintercept, we need to find out where the line represented by this equation crosses the yaxis.
Along the yaxis, x has a value of 0. This means that if we substitute x = 0 into a linear equation and find out what y equals, we will find the yintercept.
The yintercept is the constant term (here represented by the letter c, but can be any number).
More Examples of Finding the YIntercept of a Line from Linear Equations
All of the linear equations we have seen in this lesson have been in slopeintercept form (y = mx + c). This is the easiest form of linear equation to find the yintercept. You must be able to find the yintercept in all forms of linear equation. The method is the same. Substitute x = 0 into the linear equation and solve for y. The main difference is it may need more effort to rearrange the equation to solve for y.
You need to be able to find the yintercept of a linear equation in general form:
Read more about finding the yintercept from a linear equation in general form 
You need to be able to find the yintercept of a linear equation in slopepoint form:
Read more about finding the yintercept from a linear equation in slopepoint form
Positive, Zero and Negative YIntercepts
A positive yintercept means the line crosses the yaxis above the xaxis:A zero yintercept means the line crosses the yaxis at the origin:
A negative yintercept means the line crosses the yaxis below the xaxis:
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