The **intercepts** of a graph are points at which the graph crosses the axes. The ** x-intercept** is the point at which the graph crosses the

*x-*axis. At this point, the

*y-*coordinate is zero. The

**is the point at which the graph crosses the**

*y-*intercept*y-*axis. At this point, the

*x-*coordinate is zero.

To determine the *x-*intercept, we set *y *equal to zero and solve for *x*. Similarly, to determine the *y-*intercept, we set *x *equal to zero and solve for *y*. For example, lets find the intercepts of the equation [latex]y=3x - 1[/latex].

To find the *x-*intercept, set [latex]y=0[/latex].

[latex]\begin{array}{ll}y=3x - 1\hfill & \hfill \\ 0=3x - 1\hfill & \hfill \\ 1=3x\hfill & \hfill \\ \frac{1}{3}=x\hfill & \hfill \\ \left(\frac{1}{3},0\right)\hfill & x\text{-intercept}\hfill \end{array}[/latex]

To find the *y-*intercept, set [latex]x=0[/latex].

[latex]\begin{array}{l}y=3x - 1\hfill \\ y=3\left(0\right)-1\hfill \\ y=-1\hfill \\ \left(0,-1\right)y\text{-intercept}\hfill \end{array}[/latex]

We can confirm that our results make sense by observing a graph of the equation as in Figure 10. Notice that the graph crosses the axes where we predicted it would.

**Figure 12**

### How To: Given an equation, find the intercepts.

- Find the
*x*-intercept by setting [latex]y=0[/latex] and solving for [latex]x[/latex]. - Find the
*y-*intercept by setting [latex]x=0[/latex] and solving for [latex]y[/latex].

### Example 4: Finding the Intercepts of the Given Equation

Find the intercepts of the equation [latex]y=-3x - 4[/latex]. Then sketch the graph using only the intercepts.

### Solution

Set [latex]y=0[/latex] to find the *x-*intercept.

[latex]\begin{array}{l}y=-3x - 4\hfill \\ 0=-3x - 4\hfill \\ 4=-3x\hfill \\ -\frac{4}{3}=x\hfill \\ \left(-\frac{4}{3},0\right)x\text{-intercept}\hfill \end{array}[/latex]

Set [latex]x=0[/latex] to find the *y-*intercept.

[latex]\begin{array}{l}y=-3x - 4\hfill \\ y=-3\left(0\right)-4\hfill \\ y=-4\hfill \\ \left(0,-4\right)y\text{-intercept}\hfill \end{array}[/latex]

Plot both points, and draw a line passing through them as in Figure 11.

**Figure 13**

### Try It 1

Find the intercepts of the equation and sketch the graph: [latex]y=-\frac{3}{4}x+3[/latex].

Solution

Last updated on September 25th, 2020

The y-intercept of an equation is a point where the graph of the equation intersects the Y-axis. There are a few different ways to find the y-intercept with 2 points. Here is how you can find the Y-intercept with the equation from 2 points using the slope-intercept form.

Contents

### Equation from 2 points using Slope-Intercept Form

The Y-intercept with 2 points can be solved using the slope-intercept form in the equation. The point-slope form is .

### Steps

**Calculate the slope from 2 points**.For Example, Two points are (3, 5) and (6, 11)

**Substitute the slope(m)**in the slope-intercept form of the equation.**Substitute either point into the equation**. You can use either (3,5) or(6,11).**Solve for**, which is the y-intercept of the line.*b***Substitute b**, into the equation.

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## Y-Intercept

### Answers to Questions (FAQ)

### What is the y-intercept? (Definition)

The **y-intercept** is the intersection point of the function/line with the y (ordinate) axis for the abscissa value x = 0 (origin).

### How to calculate the y intercept?

**From the equation**

For any function (not necessarily affine/linear), calculate the value for $ x = 0 $. The value obtained is the **y-intercept**.

__Example:__ A curve of equation $ 3x ^ 2 + 1 $, with $ x = 0 $ is $ 3 \times 0^2 + 1 = 1 $, so 1 is the **y-intercept**

For an equation of a line of the plane, the equation has the form $ a x + b $ with $ b $ the **y-intercept**.

__Example:__ A line of equation has as **y-intercept**

**From 2 points (line only)**

With 2 points, can be calculated the equation of the line (see the linear equation calculator) and thus to deduce the **y-intercept** (see above)

**From the slope coefficient and 1 point (line only)**

Knowing the slope coefficient of a line and a point, can be deduced the equation of the line (see the linear equation calculation) and thus deduce the **y-intercept** (see above).

### Source code

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## Find Slope and y-Intercept from Equation - Process - Expii

#### (Video) Finding the Equation of a Line in Slope-Intercept Form

by Mahalo Math

Mahalo Math has a good video that explains the slope-intercept form of linear functions and equations.

#### Summary

You need a minimum of two points to be able to define a line. So, suppose we have the points: (3,−5)and(6,2)

Using these points, we want to write the equation of the line in slope intercept form which looks like: y=mx+b Here, m is the slope and b is the y-intercept.

#### Slope-Intercept Form

#### Step 1: Find the Slope

The first step is to use the two points to find the slope. We plug the points (3,−5) and (6,2) into: m=y2−y1x2−x1m=2−(−5)6−3m=73

The slope of the line between these points is 73. We can fill this in. y=73x+b

#### Step 2: Find the y-intercept

The next step is to find the y-intercept. To do this, we want to plug any one of the points on the line into the equation we have so far, y=73x+b, and solve for b.

Let's plug in the point (3,−5) and see what we get. y=73x+b−5=73(3)+b−5=7+b−12=b

Our line crosses the y-axis at (0,−12). Using this we can complete the equation of our line. y=73x−12

#### Word Problem

A parking garage charges $b, plus $m per hours parked. Carrie parks in the garage for 2 hours and pays $5. The next day, she parks for 5 hours and pays $9.50. Find m.

We know the formula for slope is: m=y2−y1x2−x1

We can plug in the given numbers to find the slope. m=y2−y1x2−x1m=($9.50−$55−2)m=($4.503)m=1.5

So, the slope of the line that represents the parking fee at the garage is m=$1.50.

## Intercept find y

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### Intro to slope-intercept form

### Video transcript

## Y Intercept

### FAQs on y Intercept

### What is Y Intercept?

The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.

### What is the slope and y Intercept of y = 6?

Comparing y=6 with y=mx+b, we get, m = 0 and b=6

Here, m is the slope of the line.

Thus, the slope of y = 6 is 0. The y intercept is 6.

### What is the *y*-intercept of y= 3x?

To find the y-intercept, substitute x=0

Then y=3(0)=0

So the y-intercept of y=3x is (0,0)

### How do you find the *y*-intercept on the graphing calculator?

We use the button "y=" on the calculator to enter the function and then press on the "graph."Then the graph of the function is displayed on the screen.

Then press on the "zoom" button.

Then press on the "trace" button and enter 0

It will then show the value of y at which x is 0

### What Is Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a function. i.e., it is used to find the point where the graph of the function cuts the x-axis. The formula to find y-intercept says that the y-intercept of a function y = f(x) can be found by substituting x = 0 in it.

### How To Derive Y Intercept Formula?

According to the definition of y-intercept, the y-intercept of a graph is the point where it cuts (or) intersects the y-axis. We know that on the y-axis the x-coordinate is 0. Hence the formula to find the y-intercept of a function y = f(x) is just substituting x = 0 and solving for y.

### What Are the Applications of Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a function. The y-intercept is mainly used in the process of graphing a function.

### Find the *y*-intercept of the graph of y= x+(1/x)?

To find the *y*-intercept of the given graph, we substitute x=0. Then we get: y=0+ 1/0 = ∞

Hence the given graph has no *y*-intercept. It means the graph does not intersect the *y*-axis anywhere.

### Find The y Intercept of The Graph represented by the equation x = y^{2}+2 y-3.

To find the y-intercept, we substitute \(x=0\) in the given equation and solve for \(y\). Then,

y^{2}+2y-3 = 0

(y+3)(y-1) = 0

y=-3

*y*-intercepts are (0, -3) and (0, 1)

### How To Use the Y Intercept Formula in Finding the Y Intercept From a Graph?

The y-intercept formula says that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it. Using this, the y-intercept of a graph is the point on the graph whose x-coordinate is 0. i.e., just look for the point where the graph intersects the y-axis and it is the y-intercept.

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