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 General Form
Question
Find the y-intercept of the line given by the linear equation shown below.Step-by-Step:
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
Answer:
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.
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.-
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 -
You need to be able to find the y-intercept of a linear equation in slope-point form:
Read more about 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: