How to Find the x-Intercept of a Line?

The $$x$$-intercept for any curve is the value of the $$x$$ coordinate of the point where the graph cuts the $$x$$-axis. The following guide learn you how to find the $$x$$-intercept of a line.

The $$x$$-intercept is the value of the $$x$$ coordinate of a point where the value of the $$y$$ coordinate is equal to zero.

Step by step guide to finding the $$x$$-intercept

In the linear equation, we read that the general form is represented by $$y=mx + b$$ that $$m$$ and $$b$$ are constant. The $$x$$-intercept is the point or the coordinate from which the line passes and that lies at the $$x$$-axis of the plane. This means the $$y$$ coordinate value of the respective linear equation will always be equal to $$0$$ when it passes through the $$x$$-axis. The $$x$$-intercept is also known as the horizontal intercept.

$$x$$-intercept formula

There are various formulas and equations for intercepts. Below are some of the most commonly used formulas. All these formulas are obtained by substituting $$y = 0$$ in the equation and solving for $$x$$.

• The general form of a straight line is $$ax+by+c=0$$,  where $$a,b,c$$ are constants. The $$x$$-intercept of the line can be obtained by putting $$y = 0$$, $$x$$-intercept $$=-\frac{c}{a}$$.
• The slope-intercept form of a straight line is as follows: $$y = mx+c$$, where $$m$$ is the slope of the line and $$c$$ is the $$y$$-intercept. The $$x$$-intercept of the line can be obtained by putting $$y=0$$, $$x$$-intercept $$= −\frac{c}{m}$$.
• The point-slope form of a straight line is $$y−b = m (x−a)$$, where $$m$$ is the slope of the line, $$(a,b)$$ is a point on the line. The $$x$$-intercept of the line can be obtained by putting $$y = 0$$, $$x$$-intercept $$= \frac{(am−b)}{m}$$.
• The intercept form of a straight line is $$\frac{x}{a} +\frac{y}{b} = 1$$ where $$(a, 0)$$ is its $$x$$-intercept and $$(0, b)$$ is its $$y$$-intercept.

$$x$$-intercept on a graph

To find the $$x$$-intercept of a line of the form $$y = mx+b$$, substitute $$y = 0$$. For example to calculate the $$x$$-intercept of the line $$y = 2x−4$$, put $$y = 0$$ in the equation of a line:

$$0=2x-4$$

$$4=2x$$

$$x=2$$

So, the $$x$$-intercept of the line $$y=2x−4$$ is $$2$$.

Find the equation of a line using $$x$$-intercept

Consider an $$x$$-intercept example to understand the process of finding the $$x$$-intercept.

Example: Find the equation of a line with the slope equal to $$2$$ and the $$x$$-intercept equal to $$-5$$.

Solution: The general equation of a line with slope $$m$$ is $$y=mx+c$$. The $$x$$-intercept of the line is $$−5$$. Using the formula of the $$x$$-intercept:

$$x=-\frac{c}{m}$$

$$-5=-\frac{c}{2}$$

$$c=10$$

By putting the value of $$c$$ and $$m$$ we have, $$y=2x+10$$.

Finding the $$x$$-Intercept – Example 1:

Find the $$x$$-intercept of the equation $$y=-3x – 4$$.

Solution:

To find the $$x$$-intercept, set $$y=0$$:

$$y=-3x-4$$

$$0=-3x-4$$

$$3x=-4$$

$$x=-\frac{4}{3}$$

Exercises for Finding the $$x$$-Intercept

1. A line with slope $$-2$$ passes through point $$P(a,1)$$. If the sum of both the intercepts of the line is equal to $$6$$, find the value of $$a$$.
2. Find the $$x$$-intercept of $$y=x^2-3x+2$$.
3. Find the $$x$$-intercept of $$y=x^2-4$$.
1. $$\color{blue}{\frac{3}{2}}$$
2. $$\color{blue}{(2,0),(1,0)}$$
3. $$\color{blue}{(2,0),(-2,0)}$$

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