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 4x2 + 9y2 = 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).
X and Y Intercept Formula
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
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