Step-by-Step Guide: Calculating X-Intercepts in Algebra Equations
Finding the x intercept is a key skill when solving maths questions involving equations, graphs, or real-life situations like budgeting or distance problems. It helps students in board exams clearly identify where a graph meets the x-axis, making plotting and interpreting data much easier.
Formula Used in x intercept
The standard formula is: \( \text{x-intercept} = \text{set } y = 0 \text{ and solve for } x \). For a line in the form \( ax + by + c = 0 \), the x-intercept is \( -\frac{c}{a} \).
Here’s a helpful table to understand x intercept more clearly:
x intercept Table
| Example Type | Equation | x intercept |
|---|---|---|
| Standard Line | y = 2x - 4 | 2 |
| Slope-Intercept Form | y = -3x + 6 | 2 |
| General Form | 3x + 2y + 12 = 0 | -4 |
| Quadratic | y = x2 - 3x + 2 | 1, 2 |
This table shows how the pattern of x intercept appears regularly in various types of equations, helping you spot it no matter how the equation is written.
Worked Example – Solving a Problem
1. Start with the equation: \( 5x + 3y + 15 = 0 \)2. Substitute \( y = 0 \) into the equation: \( 5x + 15 = 0 \)
3. Subtract 15 from both sides: \( 5x = -15 \)
4. Divide both sides by 5: \( x = -3 \)
Practice Problems
- Find the x intercept for the line: \( 4x - 7y + 8 = 0 \).
- What is the x intercept of the graph \( y = -2x + 10 \)?
- If the equation is \( y = x^2 - 5x + 6 \), list all x intercepts.
- Which value is NOT an x intercept for any equation: 0, -4, or 7?
Common Mistakes to Avoid
- Confusing x intercept with the y intercept—remember, for the x intercept, set y = 0.
- Forgetting to substitute y = 0 in non-linear equations like quadratics or rational functions.
Real-World Applications
The concept of x intercept is widely used in fields like physics (projectile motion), economics (profit and loss graphs), and engineering (design curves). Vedantu helps students practise these skills and see how intercepts are useful in real-life problem-solving and analysis.
We explored the idea of x intercept, its formulas, how to solve for it step by step, and why it is important in both exams and daily life. Practising these steps with Vedantu builds solid confidence when approaching any graph or equation problem.
If you want to learn more about related concepts such as intercepts of a line, coordinate systems like coordinate geometry, or how the gradient affects intercepts, check out these topics. For finding intercepts in different line forms, you can read about the intercept form of a line as well.
FAQs on What Is the X-Intercept and How Do You Find It?
1. What is the definition of x-intercept in mathematics?
X-intercept refers to the point where a graph or function crosses the x-axis. At this point, the value of y is always zero. In other words, it is the value of x when y = 0.
2. How do I find the x-intercept of a linear equation?
To find the x-intercept of a linear equation, follow these steps:
1. Set y = 0 in the given equation.
2. Solve for x.
For example, for the equation ax + by + c = 0, the x-intercept is x = -c/a (if a ≠ 0).
3. What is the x-intercept of 5x + 3y + 15?
Set y = 0:
5x + 15 = 0
5x = -15
x = -3
So, the x-intercept is -3. The coordinate is (-3, 0).
4. What is the x-intercept of the line 3x + 2y + 12?
Set y = 0:
3x + 12 = 0
3x = -12
x = -4
So, the x-intercept is -4. The coordinate is (-4, 0).
5. What is the formula for the x-intercept?
The x-intercept formula for a line in the form ax + by + c = 0 is:
x-intercept = -c/a, provided that a ≠ 0.
6. How are x-intercept and y-intercept different?
X-intercept is where the graph meets the x-axis (y = 0), while y-intercept is where it meets the y-axis (x = 0). Both represent points where the function cuts the respective axes.
7. What is the x-intercept in the equation y = mx + b?
Set y = 0:
0 = mx + b → x = -b/m
So, the x-intercept is x = -b/m when m ≠ 0.
8. What does the x-intercept represent on a graph?
The x-intercept on a graph represents the point(s) where the curve or line meets the x-axis. This means the value of y at this point is always zero.
9. How do you find the x-intercept of a quadratic equation?
For a quadratic equation y = ax² + bx + c, set y = 0 and solve for x using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. These values are the x-intercepts.
10. What is the x-intercept of a rational function?
For a rational function of the form f(x) = P(x)/Q(x), the x-intercepts are the values of x where P(x) = 0, provided that Q(x) ≠ 0 at those values.
11. Can a graph have more than one x-intercept?
Yes, graphs of quadratic, cubic, or higher degree polynomials can have multiple x-intercepts. Each is a point where the graph crosses or touches the x-axis.
12. How do x-intercepts and y-intercepts help in graphing equations?
Knowing x-intercepts and y-intercepts helps to sketch the basic shape of a graph quickly. These anchor points make it easier to visualize and plot the equation accurately.
