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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Created by Julia Żuławińska
Reviewed by Steven Wooding
Last updated: Apr 06, 2022
The point-slope form calculator will show you how to find the equation of a line from a point on that line and the line's slope. Soon, you will know what is point-slope form equation, and learn how is it different from the slope-intercept form equation. We also came up with two exercises, and we'll explain how to solve them in the last paragraph.
What is a slope?
Let's start with the basics. What is the slope? The slope, also known as the gradient, is the marker of a line's steepness. If it's positive, it means the line rises. If it's negative - the line decreases. If it's equal to zero, the line is horizontal.
You can find the slope between two points by estimating rise over run - the difference in height over a distance between two points.
So, slope formula is:
m = change in y / change in x = (y - y₁) / (x - x₁)
The point-slope form equation is a rearranged slope equation.
To find the gradient of non-linear functions, you can use the average rate of change calculator.
What is the point-slope form?
There is more than one way to form an equation of a straight line. Point-slope form is a form of a linear equation, where there are three characteristic numbers - two coordinates of a point on the line, and the slope of the line. The point slope form equation is:
y - y1 = m * (x - x1),
where:
- x1, y1 are the coordinates of a point, and
- m is the slope.
Do you see the similarity to the slope formula? What you might not know is that it's not the only way to form a line equation. The more popular is the slope intercept form:
y = m * x + b,
where:
- m is the slope; and
- b is the intercept of the y-axis.
The truth is that this is nothing else than a more precise point-slope form. A straight line intercepts the y-axis in a point (0, b). If you choose this point - (0, b), as a point that you want to use in the point-slope form of the equation, you will get:
y - b = m * (x - 0), which is the same as y = m * x + b.
In the two graphs below, you can see the same function, only described with two different forms of a linear equation:
How to find the equation of a line with slope and coordinates of a point?
Let's have a look at two exercises, to understand the topic more clearly.
The slope of a line is 2. It passes through point A(2, -3). What is the general equation of the line?
- Identify the point coordinates:
- x1 = 2,
- y1 = -3.
- Identify the slope:
- m = 2
- Input the values into the point slope form formula:
- y - y1 = m (x - x1)
- y - (-3) = 2(x - 2)
- Simplify to get the general equation:
- y = 2x - 4 -3
- 0 = 2x - y - 7
Let's solve an exercise with a more relatable subject.
Let's say you got a puppy. When you got him he was 14 pounds. It grew 0.2 pounds every day, and after 30 days, he was 20 pounds. Find the general equation of the puppy's growth.
- The slope is the change of weight per day: m = 0.2
- The characteristic point is 20 pounds on 30th day: (x1, y1) = (30, 20)
- Now, input the values into the point-slope formula:
y - 20 = 0.2 * (x - 30)
4. Simplify the equation to get the general equation:
0 = 0.2x - y + 14
💡 If you need to find a different point on your line click on the advanced mode button. Then, input one coordinate, and get the other.
And here you have it! We hope you enjoyed our point-slope form calculator! Before you go, check out more of our geometry calculators!
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