Point Slope Form Calculator

Point Slope form Calculator

Point slope calculator is an online tool developed to find the equation of a straight line using the slope and point on that line or two points.

What is point-slope?

Point slope form is a general form for linear equations. The equation of a line can be determined by using the point-slope form or slope intercept form. The point slope form highlights the slope of the line and a point on the line.

The slope of the line is the ratio of the change in the values of the y-axis and the change in the values of the x-axis [(y2 – y1)/(x2 – x1)]. It is used to evaluate the steepness of the line. 

You can find the equation of point-slope form in the below section.

Point slope formula

The point slope equation can be expressed as:

y - y1 = m(x- x1)

Where,

• m is the slope, and
• x1, y1 are the coordinates of a point.

How to find the equation of a line?

To find the equation of a straight line without a point slope form calculator, follow the below examples.

Example 1: For 1 point & slope

Find the equation of a line whose known points are (2, 3) and the slope of line is 8.

Solution:

Step 1: Identify and write down the values.

x₁ = 2

y₁ = 3

m = 8

Step 2: Place the values in the point slope formula and solve the equation.

y - y₁ = m(x- x₁)

y – 3 = 8(x - 2)

Further simplification

y – 3 = 8x – 16

8x – 16 – y + 3 = 0

8x – 13 – y = 0

y = 8x – 13

Example 2: For 2 points 

Evaluate the linear equation of the line whose coordinate points are (10, 15) and (12, 20)

Solution:

Step 1: Write the given points of the line.

x1 = 10

x2 = 12

y1 = 15

y2 = 20

Step 2: Evaluate the slope of the line.

m = (y₂ – y₁)/(x₂ – x₁)

m = (20 - 15)/(12 - 10)

m = 5/2 = 2.5

Step 3: Now place the slope and 1 point of the line to the point-slope equation.

y - y₁ = m(x- x₁)

y - 15 = 2.5(x - 10)

Further simplification

y - 15 = 2.5x - 25

y = 2.5x - 25 + 15

y = 2.5x - 10

FAQs

How to convert slope intercept form to point slope form?

Below are the steps to convert y=mx+c to y−y1=m(x − x1):

• Determine the Slope and Y-intercept: From the equation y=mx+c, determine the values of slope “m” and y-intercept (c).
• Use the Y-intercept as the Point: In the slope-intercept form, you always have a known point on the line: the y-intercept (0, c). You can use this point to write the equation in point-slope form.
• Input values into Point-Slope Formula: Use the y-intercept (0, c) as your x1,y1​ in the point-slope formula. y−y1​=m(x−x1​)

How to find the equation of a line with slope and point?

To find the equation of a line given a slope “m” and a point (x1, y1​), you can use the point-slope form of a linear equation:

Let's explore how to use it:

• Input the given values: Insert the known values for the slope “m” and the point (x₁, y₁) into the point-slope formula.
• Simplify the equation (optional): You can rearrange the equation to get it in slope-intercept form y=mx+c or standard form Ax+By=C, depending on your preference or the requirements of your task.

Example:

Given the point (2, 3) and a slope m = 4, let's find the equation of the line.

Solution

Input the values:

Using the point-slope form: y−3=4(x − 2)

simplify:

y−3=4x−8

y=4x−5

So, the equation of the line in slope-intercept form is y = 4x − 5.

How to convert the point-slope form to the standard form Ax+By=C?

Follow the below steps:

• Start with the point-slope form: y − y1 ​= m(x − x1​).
• Distribute the right side: y − y1 ​= mx − mx1.
• Rearrange the terms to get the equation in the form Ax + By = C If “m” is a fraction, multiply every term by the denominator to eliminate fractions.

How to graph the line from the point and the slope?

Follow these steps:

• Plot the given point (x1, y1​) on the graph.
• From this point, use the slope to determine a second point:

1. Rise = Numerator of the slope
2. Run = Denominator of the slope

For example, if the slope m = 2/3, rise 2 units up and run 3 units to the right to find your second point.

• Draw a straight line through the two points. Extend the line in both directions.

How to convert the point-slope form to the slope-intercept form y=mx+b?

Follow the below steps:

• Begin with the point-slope form: y − y1​=m(x − x1​).
• Solve for y by rearranging the terms: y = mx − mx1 ​+ y1.
• The equation will now be in the form y = mx + c, where c is the y-intercept.