Finding the Y-Intercept from a Linear Equation

The 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.

Real Examples of Finding the Y-Intercept from a Linear Equation

Finding 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 Equation

A 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).

More Examples of Finding the Y-Intercept of a Line from Linear Equations

All 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: 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: finding the y-intercept from a linear equation in slope-point form

Positive, Zero and Negative Y-Intercepts

A 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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