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)