Enter the values of X1, Y1,and (m)in the below input boxes and hit the Calculate button to get the equation of a straight line using 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 formis 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 formhighlights theslopeof the line and apointon 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 formin the below section.
Point slope formula
The point slope equation can be expressed as:
y - y1 = m(x- x1)
Where,
mis the slope, andx1,y1are the coordinates of a point.
How to find the equation of a line?
To find the equation of a straight line without a point slopeform 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 yourx1,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+cor standard formAx+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 = CIf “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:
- Rise = Numerator of the slope
- 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.
