Home » Math Vocabulary » What is Y Intercept? Definition, Formula, Equation, Examples
- What Is Y-Intercept?
- Y-Intercept Formula
- Y-Intercept of a Straight Line
- Solved Examples on Y-Intercept
- Practice Problems on Y-Intercept
- Frequently Asked Questions about Y-intercept
What Is Y-Intercept?
The y-intercept of a graph is the point where the graph crosses the y-axis.
Since the y-intercept is a point on the y-axis, its x-coordinate is always 0. Thus, the coordinates of the y-intercept are of the form (0, y).
Take a look at the y-intercept of a line on a graph shown below.
Note:
If the graph is the graph of a function, then it has at most one y-intercept. According to the vertical line test, a graph represents a function if and only if it crosses every vertical line only once. Considering the y-axis as one such vertical line, the graph of a function cannot have more than one y-intercept.
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Y-Intercept Definition
The point at which the graph function crosses the y-axis is called the y-intercept.
Related Worksheets
Y-Intercept Formula
The y intercept is of the form of (0, y). So, to find the y-intercept of a function, substitute x = 0 and solve for y.
Y-intercept example:
Let the equation of a line be y=10x+4.
Substitute x = 0.
y = 10(0) + 4
y = 0 + 4
y = 4
Thus, the y-intercept of the line is (0, 4).
Y-Intercept of a Straight Line
The y-intercept of a straight line is the point where the line intersects the y-axis. A line has only one y-intercept.
Finding the y-Intercept of a Line using General Form
The general form of the equation of the straight line is ax+by+c=0
To find y-intercept, substitute x = 0 and solve for y.
a(0)+ by + c =0
0+ by + c =0
by = -c
$y = \;-\;\frac{c}{b}$
The y-intercept of a line ax + by + c = 0 is (0, $\frac{-c}{b}$) or simply $\frac{-c}{b}$.
Finding the y-Intercept of a Line using Slope-Intercept Form
The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept of the line.
To find y-intercept, substitute x = 0 and solve for y.
y = mx + b
y = m(0) + b
y = b
The y-intercept of the equation of a line in slope-intercept form is (0, b) or b.
Finding the y-Intercept of a Line using Point-Slope Form
The point-slope form of the equation of the line is given by (y – y1) = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line.
To find y-intercept, substitute x = 0 and solve for y.
y- y1 = m(0 – x1)
y – y1 = – mx1
y = – mx1 – y1
y = y1 – mx1
The y-intercept of the a line in point-slope (y – y1) = m(x – x1) form is (0, y1 – mx1) or(y1 – mx1).
Y-Intercept on a Graph
The point where the graph crosses the y-axis is the y-intercept.
Example: The line intersects the y-axis at (0, 3). Thus, the y-intercept is (0, 3) or 3.
Y-Intercept of a Quadratic Function (Parabola)
The quadratic function has the standard form y = ax2 + bx + c. The y-intercept is always equal to the value of c.
To find the y-intercept, we just have to substitute x = 0 in the equation and solve for y. Thus, the corresponding y-intercept will be y or (0, y).
Example: y = x2 – 2x – 3
Substitute x = 0 and solve for y.
y=0 – 2(0) – 3
y = – 3
Thus, the y-intercept is -3 or (0, -3).
Facts on Y-Intercept
- To find the y-intercept, substitute x = 0 and solve for y.
- The lines parallel to the y-axis do not have the y-intercept as they don’t intersect with the y-axis.
- A function cannot have more than one y-intercept.
- The y-intercept of a polynomial function in the form y = a1 xn + a2 xn-1+ …+ an is its constant term an or (0, an).
Conclusion
In this article, we have learned about the y-intercept, definition, formula, and its different form with examples. Now, let us solve a few examples and practice problems on y-intercept.
Solved Examples on Y-Intercept
Example 1: Identify the y-intercept of the line y = 2x – 4
Solution:
To find y-intercept, substitute x = 0 and solve for y.
y = 2(0) – 12
y = -12
Thus, the y-intercept of the line y = 2x – 4 is (0,- 12).
Example 2: Find the y-intercept of the following quadratic function: y = x2 – 6x + 4
Solution:
To find y-intercept, substitute x = 0 and solve for y.
y = 02 – 6(0) + 4
y = 4
Thus, the y-intercept of the equation y = x2 – 6x + 4 is (0, 4).
Example 3: If (0,-3) is the y-intercept of the function y = 3x2 + ax + b, then find the value of b.
Solution:
Equation: y = 3x2 + ax + b
Y-intercept = (0,–3)
b = ?
Using the y-intercept formula, substitute x = 0 in the given equation,
y = 3x2 + ax + b
y = 3(0)2 + a(0) + b
y = b
Thus, b = –3
Practice Problems on Y-Intercept
1Find the y-intercept of the line y = x?
1
-1
Not defined
CorrectIncorrect
Correct answer is: 0
The y-intercept of the line y = x is 0.
y $= \frac{(0^{2}\;-\;1)}{0}$
y $= \frac{-\;1}{0}$, which is not defined.
2If the y-intercept of the line y = 5x + a is 5, then find the value of a.
3
4
5
6
CorrectIncorrect
Correct answer is: 5
Substitute x = 0 in y = 5x + a.
y = 5(0) + a
y = a
The y-intercept is a = 5.
3What is the y-intercept of the line whose equation is 4x + 6y = 10?
$\frac{2}{3}$
$\frac{5}{3}$
$\frac{3}{2}$
$\frac{3}{5}$
CorrectIncorrect
Correct answer is: $\frac{5}{3}$
Put x = 0 in 4x + 6y = 10.
0 + 6y = 10
y $= \frac{5}{3}$
Frequently Asked Questions about Y-intercept
Does a vertical line have a y-intercept?
No, a vertical line does not have a y-intercept.
What is the x-intercept of a line?
The x-intercept of a line is the point where the line crosses the x-axis.
How do you find the y-intercept of a line?
To find the y-intercept, set x equal to zero in the equation of the line and solve for y.
Is the y-intercept always a whole number?
No, the y-intercept can be any real number.