X and Y Intercept Formula (original) (raw)
Last Updated : 23 Jul, 2025
X and Y Intercept Formula as the name suggests, is the formula to calculate the intercept of a given straight line. An intercept is defined as the point at which the line or curve intersects the graph's axis. The intercept of a line is the point at which it intersects the x-axis or the y-axis.
When an equation isn't in the form y = mx + b, we determine the intercepts by substituting 0 as necessary and solving for the corresponding variable.
- To find the y-intercept, we set x = 0 and solve for y. This yields the point (0,y).
- To find the x-intercept, we set y = 0 and solve for x. This gives us the point (x,0).
Table of Content
- Intercept Definition in X and Y Intercept
- What is X-Intercept?
- X-Intercept Formula
- Derivation of X-Intercept Formula
- What is Y-Intercept?
- Y-Intercept Formula
- Derivation of Y-Intercept Formula
- How To Find X And Y Intercepts?
- Intercept Form of a Straight Line
- Intercept Graph
- For Point-Slope Form
- Uses of X And Y Intercept
- Solved Example of X and Y Intercept Formula
- Practice Problems on X and Y Intercept Formula
Intercept Definition in X and Y Intercept
An intercept is defined as the point where the line or curve crosses the axis. If the point is on the x-axis then it is called the x-intercept and if the point is on the y-axis, then it is called the y-intercept.
We generally represent the x-intercept by **a and the y-intercept by **b. The equation of the line making a and b intercept on the x and y axis respectively is,
**x/a + y/b = 1
What is X-Intercept?
The x-intercept of a line is the point at which the line intersects the x-axis. So, to find the x-intercept put y = 0 in the equation of a line.
X-Intercept Formula
The formula of x-intercept for slope-intercept equation y = mx + c is given by,
X-Intercept Formula
**x-intercept = -c/m
Thus, ****(-c/m, 0)** is the coordinate of x-intercept.
Where,
- ****(0, c)** is the y-intercept,
- **m is the slope of the given line.
**Derivation of X-Intercept Formula
Consider a line given in the slope intercept form y = mx + c, where the line has a intercept (c, 0) and has a slope m.
Put y = 0 in the equation to get the x-intercept.
⇒ 0 = mx + c
Solve the equation for x.
⇒ mx = -c
⇒ x = -c/m
This derives the formula for x-intercept.
**Check: **Slope Intercept Form of line
What is Y-Intercept?
The y-intercept of a line is the point at which the line intersects the y-axis. So, to find the y-intercept, put x = 0 in the equation of a line.
Y-Intercept Formula
The formula of y-intercept for slope-intercept equation y = mx + c is given by,
Y-Intercept Formula
**y-intercept = c
Thus, ****(0, c)** is the coordinate of y-intercept.
**Derivation of Y-Intercept Formula
Consider a line given in the slope-intercept form y = mx + c, where the line passes through the point (0, c) and has a slope m.
Put x = 0 in the equation to get the y-intercept.
⇒ y = m (0) + c
⇒ y = 0 + c
⇒ y = c
This derives the formula for y-intercept.
How To Find X And Y Intercepts?
To find the x-intercept we put y = 0 in the given function and then solve for x. The resultant value of x is the x-intercept of the given function.
**Example: Find the x-intercept of the linear equation 2x + 3y = 7.
**Solution:
For the x-intercept of the linear equation 2x + 3y = 7
Put y = 0,
2x + 3×0 = 7
⇒ x = 7/2
Thus, the x-intercept of 2x + 3y = 7 is 7/2.
To find the y-intercept we put x = 0 in the given function and then solve for y. The resultant value of y is the y-intercept of the given function.
**Example: Find the y-intercept of the linear equation 3x + 4y = 12.
**Solution:
For the y-intercept of the linear equation 3x + 4y = 12
Put x = 0,
3×0 + 4y = 12
⇒ y = 12/4
⇒ y = 3
Thus, the y-intercept of 3x + 4y = 12 is 3.
Intercept Form of a Straight Line
Intercept Form of a Straight Line, mathematically given by
**x/a + y/b = 1
Where,
- **a is the x-intercept of the straight line
- **b is the y-intercept of the straight line
Intercept Graph
We know that the intercept is the points on the axes that are cut by a straight line. The point on the x-axis is called the x-intercept, and the point on the y-axis is called the y-intercept. The image added below shows the line, with x and y intercepts.
For Point-Slope Form
The point-slope form of a line is given as follows:
**y - y 1 = m(x - x 1 )
where:
- ****(x** 1 , y 1 ) is a point on the line
- **m is the slope of the line.
To find, the x and y-intercepts of the given line,
Here, rearranging the equation, we get
y = mx - mx1 + y1
⇒ y = mx + (-mx1 + y1)
Comparing it with y = mx + c, we get
c = -mx1 + y1, which is the y-intercept of the given line.
and x-intercept is -c/m = (mx1 - y1)/m = x1 - y1/m
Thus, x and y-intercept of the given **y - y 1 = m(x - x 1 ) are **x 1 **- y 1 /m and **-mx 1 **+ y 1respectively.
Uses of X And Y Intercept
There are various use cases of X And Y Intercepts, some of which are as follows:
- We use the concept of intercepts in curve tracing, for example, we have an unknown curve, so intercepts are one of the first parameters in the analysis of the curve.
- Both intercepts in whichever quadrant forms a triangle, whose area can calculate by 1/2 times the product of intercepts.
- By plotting both intercepts on the coordinated axes, we can plot the graph of the linear equation.
**Articles related to X and Y Intercept Formula:
Solved Example of X and Y Intercept Formula
**Problem 1: Calculate the x-intercept of the equation x + 3y = 8.
**Solution:
We have the equation as, x + 3y = 8.
Put y = 0 to find the x-intercept and then solve the equation for x.
⇒ x + 3 (0) = 8
⇒ x = 8
So, the x-intercept for the equation is (8, 0).
**Problem 2: Calculate the x-intercept of equation 4x + 7y = 10.
**Solution:
We have the equation as, 4x + 7y = 10.
Put y = 0 to find the x-intercept and then solve the equation for x.
⇒ 4x + 7 (0) = 10
⇒ 4x = 10
⇒ x = 10/4
⇒ x = 5/2
So, the x-intercept for the equation is (5/2, 0).
**Problem 3: Calculate the y-intercept of equation 4x + 3y = 24.
**Solution:
We have the equation as, 4x + 3y = 24.
Put x = 0 to find the y-intercept and then solve the equation for y.
⇒ 4(0) + 3y = 24
⇒ 3y = 24
⇒ y = 24/3
⇒ y = 8
So, the y-intercept for the equation is (0, 8).
**Problem 4: Calculate the y-intercept of equation 8x + 5y = 25.
**Solution:
We have the equation as, 8x + 5y = 25.
Put x = 0 to find the y-intercept and then solve the equation for y.
⇒ 8(0) + 5y = 25
⇒ 5y = 25
⇒ y = 25/5
⇒ y = 5
So, the y-intercept for the equation is (0, 5).
**Problem 5: Calculate the x- and y-intercept of equation 4x 2 + 9y 2 = 25.
**Solution:
We have the equation as, 4x2 + 9y2 = 25.
Put y = 0 to find the x-intercept and then solve the equation for x.
⇒ 4x2 + 9 (0)2 = 25
⇒ 4x2 = 25
⇒ x2 = 25/4
⇒ x = ±5/2
So, the x-intercept for the equation is (±5/2, 0).
Put x = 0 to find the y-intercept and then solve the equation for y.
⇒ 4 (0)2 + 9y2 = 25
⇒ 9y2 = 25
⇒ y2 = 25/9
⇒ y = ±5/3
So, the y-intercept for the equation is (0, ±5/3).
Practice Problems on X and Y Intercept Formula
**1. Find the x and y intercepts of the equation 3x - 2y = 6
**2. Determine the x and y intercepts of the line represented by the equation 2y + 4x = 8
**3. Find the x and y intercepts of the equation y = 2x - 3
**4. Determine the x and y intercepts of the line represented by the equation 4x + 3y = 12
**5. Find the x and y intercepts of the equation 5y - 2x = 10