Slope intercept form with two points calculator

Find the slope intercept equation of a line (y=mx+b or y=mx+c) from two points with this slope intercept form calculator.

Slope Intercept Form Equation: y = mx + b, or sometimes y = mx + c,

m = slope (the amount of rise over run of the line)
b= y-axis intercept ( where the line crosses over the y-axis)

To calculate the slope intercept form equation from two coordinates
(x1,y1) and (x2,y2):

Step 1: Calculate the slope (y2 - y1) / (x2 - x1)

Step 2: Calculate where the line intersects with the y-axis by
entering one of the coordinates into this equation: y - mx = b

Example:

To calculate the slope-intercept equation for a line that includes
the two points ( 7, 4) and (1, 1).

Step 1: slope (m) = (1 - 4) / (1 - 7) = -3 / -6

slope (m) = -3/-6 = 1/2

Step 2: Using one of the original coordinates (7, 4) we find the
y-axis intercept (b) using the formula: y - mx = b

y=4, m=1/2, x =7

y - mx = b

b= .5

The slope intercept form for this line is y = .5x + .5

This line crosses the y-axis at .5 and has a slope of .5,
so this line rises one unit along the y-axis for every 2 units
it moves along the x-axis.

So, where would you ever use this? Here's an article on ways to use the Slope Intercept Form in Real Life.

You can find an equation of a straight line given two points laying on that line. However, there exist different forms for a line equation. Here you can find two calculators for an equation of a line:

• first calculator finds the line equation in slope-intercept form, that is,
  
  It also outputs slope and intercept parameters and displays the line on a graph.

• second calculator finds the line equation in parametric form, that is,
  
  It also outputs a direction vector and displays line and direction vector on a graph.

Also, the text and formulas below the calculators describe how to find the equation of a line from two points manually.

Slope-intercept line equation from two points

First Point

Second point

Calculation precision

Digits after the decimal point: 2

Parametric line equation from two points

First Point

Second point

Calculation precision

Digits after the decimal point: 2

How to find the equation of a line in slope-intercept form

Let's find slope-intercept form of a line equation from the two known points and .
We need to find slope a and intercept b.
For two known points we have two equations in respect to a and b

Let's subtract the first from the second

And from there

Note that b can be expressed like this

So, once we have a, it is easy to calculate b simply by plugging or to the expression above.

Finally, we use the calculated a and b to write the result as

Equation of a vertical line

Note that in the case of a vertical line, the slope and the intercept are undefined because the line runs parallel to the y-axis. The line equation, in this case, becomes

Equation of a horizontal line

Note that in the case of a horizontal line, the slope is zero and the intercept is equal to the y-coordinate of points because the line runs parallel to the x-axis. The line equation, in this case, becomes

How to find the slope-intercept equation of a line example

Problem: Find the equation of a line in the slope-intercept form given points (-1, 1) and (2, 4)
Solution:

1. Calculate the slope a:
   
2. Calculate the intercept b using coordinates of either point. Here we use the coordinates (-1, 1):
   
3. Write the final line equation (we omit the slope, because it equals one):
   

And here is how you should enter this problem into the calculator above: slope-intercept line equation example

Parametric line equations

Let's find out parametric form of a line equation from the two known points and .
We need to find components of the direction vector also known as displacement vector.

This vector quantifies the distance and direction of an imaginary motion along a straight line from the first point to the second point.

Once we have direction vector from to , our parametric equations will be

Note that if , then and if , then

Equation of a vertical line

Note that in the case of a vertical line, the horizontal displacement is zero because the line runs parallel to the y-axis. The line equations, in this case, become

Equation of a horizontal line

Note that in the case of a horizontal line, the vertical displacement is zero because the line runs parallel to the x-axis. The line equations, in this case, become

How to find the parametric equation of a line example

Problem: Find the equation of a line in the parametric form given points (-1, 1) and (2, 4)
Solution:

1. Calculate the displacement vector:
   
2. Write the final line equations:
   

How do you find slope

What is the slope

How do I find the y