Point Slope Form Calculator

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The point slope form calculator determines the point slope between two points in the Cartesian coordinate system. It uses coordinates of a point A\(\left(y-y_1\right)\) and slope m in the two-dimensional Cartesian coordinate plane and find the equation of a line that passes through A.

In this post, we will explain what point slope is, how to use point slope calculator, how to calculate point slope form, point slope form equation, and much more.

How to use our point slope form calculator?

It can be very tricky and inconvenient to find the point slop by manual calculations. To use the point slope equation calculator, follow the steps given below:

  • Enter a value for \(X_1\) in the first input box.
  • Enter a value for \(Y_1\) in the second input box.
  • Enter the slope value.
  • Press the Calculate button to get the point slope form for the given coordinates.

It will instantly give you a point of slope for the given values.

What is point slope form?

The point slope form is defined as the difference between two points\(\left(y-y_1\right)\) on a line in the y-axis coordinate is proportional to the difference in the x-axis coordinate points \(\left(x-x_1\right)\) , and the proportionality constant m is the point slope of the straight line.

Point slope formula

The formula for point slope through point A\(\left(x_1,y_1\right)\) can be written as follow:

 \(y  –  y_1 =\dfrac{m}{x  –  x_1} \)

The above equation can be transformed into the slope of a line formula as follow:

\(m = \dfrac{y  –  y_1}{x  –  x_1}\)

How to find point slope form?

The point slope form can be calculated by using the above formula. You will be needing the slope of the line and coordinated for X and Y to find the point slope form. To calculate the slope of the line, you can also use our slope calculator. Follow the steps below to calculate the point slope intercept form.

  1. Identify the coordinates for both X and Y.
  2. Identify the slope of the line.
  3. Enter the values in the point slope formula to get the equation of point slope form.

Example:

Suppose we have the coordinates of \(\left(x,y_1\right)\) as \(\left(-6,8\right)\) and the slope is 5. Let’s calculate the point slope form by using given values.

Step 1: Identify the coordinates. Here we have:

\( x_1 =6, and  y_1 = 8\)

Step 2: Identify the slope of line.

\(m= 5\)

Step 3: Place all values in the point slope form equation.

\(y  –  y_1 =\dfrac{m}{x  –  x_1} \)

\( y - 8 = \dfrac{5}{x  – \left(-6\right)} \)

\( y - 8 = \dfrac{5}{x + 6}\)

\( y - 8 = 5x + 30\)

\(5x + 30 -y + 8\)

\(5x - y + 38\)

So the point slope equation for coordinates \(\left(-6,8\right)\) , and slope 5 will be \(5x - y + 38.\)

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Point Slope Form Calculator

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