# Point Slope Form Calculator

Point Slope Form Calculator is an online tool that helps to calculate the equation of a line that passes through a given point when the slope of the line is known. A linear equation in two variables is used to represent the equation of a line.

## What is the Point Slope Form Calculator?

Point Slope Form Calculator helps to determine the equation of a line with a given slope and a given point that is on the line. Each and every point that lies on a straight line must satisfy the equation of that straight line. To use the **point slope form calculator**, enter the values in the given input boxes.

### Point Slope Form Calculator

## How to Use Point Slope Form Calculator?

Please follow the steps given below to find the equation of a line using the point slope form calculator:

**Step 1:**Go to Cuemath's online point slope form calculator.**Step 2:**Enter the \(x_{1}\) and \(y_{1}\) coordinates as well as the slope in the given input boxes.**Step 3:**Click on the**"Calculate"**button to find the equation of a line.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Point Slope Calculator Work?

The slope of a line can be defined as the steepness of the line with respect to the horizontal. Depending upon the information available the equation of a line can be determined using different methods. These are point-slope form, two-point form, normal form, intercept form, and slope-intercept form. If we have a line with slope 'm' that passes through a fixed point whose coordinates are given by (\(x_{1}\), \(y_{1}\)), then the point-slope form of the line is given by:

y - \(y_{1}\) = m (x - \(x_{1}\)).

Here (x, y) must be kept as variables as they denote any random point on the line.

The steps to find the equation of a line by using the point-slope form are given as follows:

- Note down the slope 'm' of the line as well as the given coordinates, (\(x_{1}\), \(y_{1}\)) of the point on the line.
- Substitute these values in the aforementioned equation.
- Simplify the equation.
- Keep the variable terms on the left and the constant terms on the right to get the equation of the line.

## Solved Examples on Point Slope Form

**Example 1:**

Find the equation of a line with slope 3 that passes through a point (2, 3) and verify it using the point slope form calculator.

**Solution:**

The equation of the point-slope form is: y - \(y_{1}\) = m (x - \(x_{1}\))

y - 3 = 3 (x - 2)

y − 3 = 3x - 6

3x - y = 3

Therefore, the equation of line is 3x - y = 3

**Example 2:**

Find the equation of a line with slope 5/2 that passes through a point (-12, 4) and verify it using the point slope form calculator.

**Solution:**

The equation of the point-slope form is: y - \(y_{1}\) = m (x - \(x_{1}\))

m = 5/2 = 2.5

y - 4 = 2.5 (x - (-12))

y - 4 = 2.5x + 30

-2.5x + y = 34

Therefore, the equation of line is -2.5x + y = 34

Similarly, you can try the point slope form calculator to find the equation of a line if

- Slope m = -4.2, coordinates (5,8)
- Slope m = 8, coordinates (-7,4)

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