# Finding the Y-Intercept from a Linear Equation in General Form(KS3, Year 9)

homesitemaplinear equationsfinding the y-intercept from a linear equation in general form
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.

## Question

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

## 1

Substitute x = 0 into the linear equation 3x + 2y + 4 = 0. This gets rid of the term with x in it.

3(0) + 2y + 4 = 0

2y + 4 = 0

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

## 2

Subtract 4 from both sides.

2y + 4 − 4 = 0 − 4

2y = −4

## 3

Divide both sides by the 2 in front of the y.

2y ÷ 2 = −4 ÷ 2

y = −2

The y-intercept of the line given by the linear equation 3x + 2y + 4 = 0 is −2.

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

A linear equation (in general 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 general form (ax + b + c = 0). 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:

## Interactive Widget

You can use this interactive widget to create a graph of your linear equation. Use the buttons to change the values of the linear equation.
Change the Equation
y
x
y-intercept

This page was written by Stephen Clarke.

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