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 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
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_{1} = m(x − x_{1})). 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 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: