How to Find the y-Intercept of a Line?

An intercept of a function is a point where the graph of the function cuts the axis. The \(y\)-intercept of a function is a point where its graph would meet the \(y\)-axis.

A step-by-step guide to finding the \(y\)-intercept

The \(y\) intercept of a graph is the point where the graph intersects the \(y\)-axis. We know that the \(x\)-coordinate of any point on the \(y\)-axis is \(0\). So the \(x\)-coordinate of a \(y\)-intercept is \(0\). 

\(y\)-intercept Formula

The \(y\)-intercept of a function is a point where its graph would meet the \(y\)-axis. The \(x\)-coordinate of any point on the \(y\)-axis is \(0\) and we use this fact to derive the formula to find the y-intercept. i.e., the \(y\)-intercept of a function is of the form \((0, y)\).

Here are the steps to find the \(y\)-intercept of a function \(y = f(x)\),

• Substitute \(x = 0\) in it.
• Solve for \(y\).
• Represent the \(y\)-intercept as the point \((0, y)\).

How to find \(y\)-intercept?

We just substitute \(x=0\) in the equation of the line and solve for \(y\). Then the corresponding \(y\)-intercept is \(y\) or \((0, y)\).

\(y\)-intercept of a quadratic function (parabola)

The method for finding the \(y\)-intercept of a quadratic function or the \(y\)-intercept of a parabola is the same as that of a line. If a quadratic equation is given, substitute \(x = 0\) and solve for \(y\) to get the \(y\) intercept.

Finding the \(y\)-Intercept – Example 1:

Find the \(y\)-intercept of the equation \(y=x^2-2x-3\).

Solution:

Substitute \(x=0\) and solve for \(y\):

\(y=0^2-2(0)-3\)

\(y=-3\)

So, the \(y\)-intercept is \(-3\) or \((0,-3)\).

Exercises for Finding the \(y\)-Intercept

1. Find the \(y\)-intercept of the equation \(y=(x^2-1)\).
2. If the \(y\)-intercept of the function \(y=3x^2+ax+b\) is \((0,-5)\), find the value of \(b\).
3. Find the \(y\)-intercept of the equation \(3x+(-2y)=12\).

1. \(\color{blue}{(0,-1)}\)
2. \(\color{blue}{-5}\)
3. \(\color{blue}{-6}\)