Intercepts of a Line

What is the Intercept of a Line?

The x-intercept and the y-intercept are the two different types of intercepts. The line's actual point of intersection with the x-axis is known as the x-intercept, while its actual point of intersection with the y-axis is known as the y-intercept. In this article, we will define the intercept, show how to obtain the intercept for a given line, and demonstrate how to graph intercepts.

What is x-Intercept?

The general form of the linear equation is written as $$y=mx+c$$, where m and c are constants. The line's crossing point, which is located at the x-axis of the plane, is known as the x-intercept. This indicates that anytime a linear equation crosses the x-axis, its y-coordinate value will always be equal to 0. The y-coordinate is zero for the x-intercept and the x-coordinate is zero for the y-intercept. The term "horizontal intercept" also applies to the x-intercept.

X-Intercept

What is y- Intercept?

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula $$y=f\left(x\right)$$ is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

Y-Intercept

Equation of a Line with Intercepts

How to find an intercept of a straight line? Intercepts are subject to various equations and formulas. By solving for x and putting $$y=0$$ in the equation, all of the formulas are obtained.

Following are the steps to determine the y intercept of a function, where$$y=f\left(x\right)$$, where $$x=0$$ is simply substituted.

Resolve for y.

Put the y-point intercepts in place (0, y).

Intercepts

Conclusion

The two different kinds of intercepts are the x-intercept and the y-intercept. The x-intercept of a line is its actual point of intersection with the x-axis, and the y-intercept is its true point of intersection with the y-axis.

Solved Examples

Example 1:Find the value of "a" if the y-intercept of a function $$y=a(x-1)\left(x-2\right)\left(x-3\right)$$ is $$\left(0,12\right)$$ .

Ans: The given function's equation is:

$$y=a(x-1)\left(x-2\right)\left(x-3\right)$$

By adding $$x=0$$ to the y-intercept formula, it can be calculated.

$$y=a\left(0-1\right]\left[0-2\right]\left[0-3\right]$$ $$=-6a$$

The y-intercept is therefore $$\left(0,-6a\right)$$

However, the issue claims that the provided function's y-intercept is $$\left(0,12\right)$$. Thus,

$$-6a=12$$

Using -6 to divide both sides,

$$a=-2$$

Example 2: Find the x and y intercept in the given graph.

Ans: The x-intercept is 7 and y – intercept is 3.5 in the given graph.

Example 3: Find the x-intercept of $$y=4x-8$$.

Ans: For finding the x – intercept we must put y coordinate as 0.

Thus, putting$$y=0$$ ,we will get:

$$\begin{array}{l}0=4x-8\\ 8=4x\\ x=2\end{array}$$

Therefore, x coordinate is 2.