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

The Lesson

The y-intercept is where a line crosses the y-axis.

The y-intercept is where the 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.
3 x plus 2 y plus 4 equals 0

Step-by-Step:

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

Answer:

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

y-intercept on a graph

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:

y minus y 1 equals m ( x minus x 1 ) To find the y-intercept, we need to find out where the line represented by this equation crosses the y-axis.

x equals 0 at 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:

positive y intercept A zero y-intercept means the line crosses the y-axis at the origin:

zero y-intercept A negative y-intercept means the line crosses the y-axis below the x-axis:

negative y-intercept
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See Also

What is the y-intercept? What is the y-coordinate? What is the y-axis? What is a linear equation in slope-point form?