# How to Find the y-Intercept of a Line?

The $$y$$-intercept is the point where the graph intersects the $$y$$-axis. The following guide learn you 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. $$\color{blue}{-6}$$

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