## The Lesson

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.

## How to Find the Y-Intercept from a Linear Equation in Slope-Point Form

Finding the y-intercept of a line from a linear equation in slope-point form is easy.

## Question

Find the y-intercept of the line given by the linear equation shown below.

# 1

Substitute x = 0 into the linear equation y − 4 = 2(x − 1). This gets rid of the term with x in it.

y − 4 = 2(0 − 1)

y − 4 = 2(−1)

We now want to solve for y. We need to rearrange the equation using algebra to find y =.

# 2

Evaluate the right hand side by multiplying the number before the brackets with the number inside the bracket.

y − 4 = 2(−1) = 2 × (−1)

y − 4 = −2

Don't forget: A positive number multiplied by a negative number equals a negative number.

# 3

Add 4 to both sides (because 4 is the number being subtracted from y).

y − 4 + 4 = −2 + 4

y = 2

The y-intercept of the line given by the linear equation y − 4 = 2(x − 1) is 2.

## Understanding Finding the Y-Intercept from a Linear Equation in Slope-Point Form

A linear equation (in slope-point 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.

## Lesson Slides

The 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 Equations

All of the linear equations we have seen in this lesson have been in slope-point form (y − y1 = m(x − x1)). There are other forms of linear equation. 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.

## 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: