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.

A 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.

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. \(\color{blue}{(2,0),(-2,0)}\)