Finding the Y-Intercept from a Linear Equation
(KS3, Year 9)
The LessonThe y-intercept is where a line crosses the y-axis.
A line can be represented by a linear equation. We can find the y-intercept from a linear equation.
Interactive WidgetYou can use this interactive widget to create a graph of a linear equation and see its y-intercept. Use the buttons to change the values of the linear equation.
Real Examples of Finding the Y-Intercept from a Linear EquationFinding the y-intercept of a line from a linear equation is easy. Here are some linear equations, which represent lines. We show how to find the y-intercept from the linear equation.
The y-intercept 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 y-intercept.
The y-intercept of y = −3x + 3 is 3.
The y-intercept of y = x − 2 is −2.
Look at the sign in front of the constant. If it is a minus sign (−) the y-intercept must also have a minus sign. The y-intercept is negative; it is below the x-axis.
The y-intercept of y = 4x is 0.
There is no constant term. The y-intercept is 0.
Understanding Finding the Y-Intercept from a Linear EquationA linear equation (in slope-intercept form) is given in the form below:
To find the y-intercept, we need to find out where the line represented by this equation crosses the y-axis.
Along the y-axis, 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 y-intercept.
The y-intercept is the constant term (here represented by the letter c, but can be any number).
Lesson SlidesThe slider below gives a real example of how to find the y-intercept from a linear equation. Open the slider in a new tab
More Examples of Finding the Y-Intercept of a Line from Linear EquationsAll of the linear equations we have seen in this lesson have been in slope-intercept form (y = mx + c). This is the easiest form of linear equation to find the y-intercept. You must be able to find the y-intercept 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 y-intercept of a linear equation in general form:
Read more about finding the y-intercept from a linear equation in general form
You need to be able to find the y-intercept of a linear equation in slope-point form:
Read more about finding the y-intercept from a linear equation in slope-point form
Positive, Zero and Negative Y-InterceptsA positive y-intercept means the line crosses the y-axis above the x-axis:
A zero y-intercept means the line crosses the y-axis at the origin:
A negative y-intercept means the line crosses the y-axis below the x-axis:
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