## 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.## Step-by-Step:

# 1

Substitute
We now want to solve for

**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)

**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

## Answer:

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.

## 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 − y**). 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

_{1}= m(x − x_{1})**x = 0**into the linear equation and 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-intercept form: Read more about finding the y-intercept from a linear equation in slope-intercept 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: