Point slope form Calculator

Point slope form calculator with two points

A point-Slope form calculator gives the difference between two points of a line. It uses a point and slope to give you a linear equation. The calculator has an easy interface to avoid any confusion and trouble.

This point-slope form equation calculator provides you with a number of things related to the linear equation. Those are:

1. Point slope form
2. Slope intercept form 
3. Standard form
4. Graph of the line

Let’s learn what the point-slope form is and how to derive the point-slope form using the slope formula.

What is the point-slope form?

A line can be represented mathematically or more specifically algebraically in many ways. That means it has more than one linear equation.

All of these equations can be simplified or converted to one another with the right technique. 

Point slope form is also one of those many equations. The name comes from the fact that it is derived from the slope and a point on the line. Its general form is:

Y - Y₁ = m (X - X₁)

Where m is the slope and the point (y₁, x₁) is often a known coordinate point. For a more concrete example, assume a random point and slope, let’s say (3,4) and -1.

The point-slope equation for this line will be:

Y - 4 = (-1) (X - 3)

If you have this type of equation of the line then you can easily know the slope and one point on the line by merely looking at it.

Derivation of the point-slope form:

For the derivation of the equation of a line, we will obviously need to assume some information. Consider that you have a line with a slope of m and a point (X₁, Y₁). 

Now, we know the slope is rise overrun. To write its formula we will have to let another point be (X, Y). The formula of the slope is:

m = (Y - Y₁) / (X - X₁)

This is already an equation. But to simplify it more, we remove the denominator of the right-hand side and multiply it to the left as;

m(X - X₁) = (Y - Y₁)  OR  (Y - Y₁) = m(X - X₁)

This is the point-slope form. It is one of the initial stages of the derivation of slope-intercept form. So, if we keep solving we will eventually derive the slope-intercept form as well. 

But let’s do a more realistic example with some actual values. Let the point be (2,3) and slope by 4.

Putting these values in the slope formula or use a slope calculator.

m = (Y - Y₁) / (X - X₁)
4 = (Y - 3) / (X - 2)

Making the point-slope form
 (Y - Y₁) = m(X - X₁)
 (Y - 3) = 4(X - 2)

Multiplying 4 with the parentheses. 
(Y - 3) = 4X - 8
Y = 4X - 8 + 3
Y = 4X - 5

This is the slope-intercept form where the coefficient of x is the slope and constant 5 is the y-intercept. Now, by rearranging we get:

Y - 4X + 5 = 0

It is the standard form of the equation.

How to find the point-slope form?

You can use the point-slope form calculator to find the equation. See an example for a manual calculation. 

Example:
Find the slope-intercept form of the linear equation with slope 5. One point on the line is (1, 8).

Solution:
Step 1: Write the given data.

Point; X1 = 1 and Y1 = 8
Slope = 5

Step 2: Put the values in the general point-slope form.

(Y - Y₁) = m(X - X₁)

Y - 8 = 5(X - 1)  -----------------------   point slope form 
Y = 5X - 1 + 8
Y = 5X + 7        -----------------------   slope intercept form 
= 5X + 7 - Y      -----------------------   Standard form