Write an equation of the line with the given slope and y intercept

Enter the values in the below calculator. Hit the Calculate button to get the slope intercept form of a line using y=mx+b equation.

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Slope intercept form calculator is an online tool that is used to find slope intercept form (equation of line) using two points, y-intercept, or one point and slope.

What is slope intercept form?

Slope intercept is a form of linear equation that can be used to find the equation of a straight line with y intercept and slope of line.

Slope intercept formula

The slope intercept equation can be represented as:

y = mx + b

Where,

x, y represents the x and y coordinates,

m is slope of line, and

b is y intercept.

The equation of slope intercept varies in USA and UK. In UK, variable c is used to represent y-intercept.

 y = mx + c

How to find the slope intercept form (equation of a straight line)?

To find equation of a straight line with slope and y-intercept, follow the example below.

Example:

Find the Straight line equation if y-intercept is 6 and slope is 4.

Solution:

Step 1:Identify the values.

b = 6

m = 4

Step 2:Write the slope form equation and place the values.

y = mx + b

y = 4x + 6

If you need to calculate the slope using two points, use slope calculator.

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Interpreting Lines:

This is an introduction to drawing lines when given the slope and the y-intercept in an equation form. Remember that the y-intercept is where the graph crosses the y-axis; this is where we usually start. First, find the y-intercept, then determine the slope. For now, just focus on whether the slope is positive or negative.

Here are the variables we will start using in our function:

• m = slope
• b = y-intercept

The equation is y = mx + b. The x and y variables remain as letters, but m and b are replaced by numbers (ex: y = 2x + 4, slope = 2 and y-intercept = 4). The following video will show a few examples of understanding how to use the slope and intercept from an equation.

Video Source (03:53 mins) | Transcript

y = mx + b

This equation is called the slope-intercept form because the two numbers in the equation are the slope and the intercept. Remember, the slope (m) is the number being multiplied to x and the intercept (b) is the number being added or subtracted.

Additional Resources

• Khan Academy: Intro to Slope-Intercept Form (08:59 mins; Transcript)
• Khan Academy: Worked Examples: Slope-Intercept Intro (04:39 mins; Transcript)

Practice Problems

1. Find the slope of the line:
   \(\text{y}=6\text{x}+2\)


2. Find the y-intercept of the line:
   \({\text{y}}=-7{\text{x}}+4\)


3. Find the slope of the line:
   \({\text{y}}=-3{\text{x}}+5\)


4. Find the y-intercept of the line:
   \({\text{y}}=-{\text{x}}-3\)

The Algebra of Lines:

In this lesson, we learn how to graph our line using the y-intercept and the slope. First, we know that the y-intercept (b) is on the y-axis, so we graph that point. Next, we use the slope to find a second point in relation to that intercept. The following video will show you how this is done with two examples.

Video Source (05:37 mins) | Transcript

Steps for graphing an equation using the slope and y-intercept:

1. Find the y-intercept = b of the equation y = mx + b.
2. Plot the y-intercept. The point will be (0, b).
3. Find the slope=m of the equation y = mx + b.
4. Make a single step, using the rise and run from the slope. (Make sure you go up to the right if it’s positive and down to the right if it’s negative.)
5. Connect those two points with your line.

Additional Resources

• Khan Academy: Intro to Slope-intercept Form (08:59 mins, Transcript)
• Khan Academy: Graph from Slope-intercept Equations (03:01 mins, Transcript)
• Khan Academy: Slope-intercept Examples (03:45 mins, Transcript)

Practice Problems

1. Plot the line \({\text{y}}=-3{\text{x}}+2\) starting with the y-intercept and then using the slope.
2. Plot the line \({\text{y}}=\frac{1}{2}{\text{x}}-3\) starting with the y-intercept and then using the slope.
3. Plot the line \({\text{y}}=-\frac{3}{5}{\text{x}}+1\) starting with the y-intercept and then using the slope.
4. Plot the line \({\text{y}}=2{\text{x}}+3\) starting with the y-intercept and then using the slope.
5. Plot the line \({\text{y}}=-{\text{x}}-4\) starting with the y-intercept and then using the slope.
6. Plot the line \({\text{y}}=\frac{4}{5}{\text{x}}+4\) starting with the y-intercept and then using the slope.

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