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
- Find the slope of the line:
\(\text{y}=6\text{x}+2\) - Find the y-intercept of the line:
\({\text{y}}=-7{\text{x}}+4\) - Find the slope of the line:
\({\text{y}}=-3{\text{x}}+5\) - 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:
- Find the y-intercept = b of the equation y = mx + b.
- Plot the y-intercept. The point will be (0, b).
- Find the slope=m of the equation y = mx + b.
- 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.)
- 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
- Plot the line \({\text{y}}=-3{\text{x}}+2\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=\frac{1}{2}{\text{x}}-3\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=-\frac{3}{5}{\text{x}}+1\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=2{\text{x}}+3\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=-{\text{x}}-4\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=\frac{4}{5}{\text{x}}+4\) starting with the y-intercept and then using the slope.