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What is Point Slope Form?

Albert by Albert
February 5, 2022
in Education
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There are three ways to determine the equation of a straight line. Here, we will discuss the point slop form to find out the equation of a straight line. The point-slope form of the equation of a straight line is represented as:

Point- Slope Form Equation: y – y₁ = m (x – x₁)

The above equation is useful when we know :

  • One point on the line i.e (x₁, y₁)
  • The slope of a line i.e. ‘m’

What Does The Point In The Equation Stands For?

  • (x₁, y₁): These are the known points.
  • ‘M’ represents the slope of the line
  • (x,y): These are any other points on the line.

Point Slope Form Derivation

Slope (m): Change in yChange in x

This gives y – y₁ x – x₁

Let us start with the slope:    y – y₁ x – x₁= m

Rearranging by placing the denominator on the right side of the equation, we get the desired point-slope form equation as:  y – y₁ = m (x – x₁)

Let us learn to find the equation of a line using the point-slope form with the help of  an example:

Example:

Using the point-slope form, find the equation of a straight line that passes through the point (1,4) with the slope -5.

Solution:

Here, 

y₁ = 4

x₁ = 1

m = -5

Using the point-slope form method, we get the equation as:

(y – 4) =  -5 (x – 1)

y – 4 =  -5x + 5

y = -5x + 5 + 4

y = -5x + 9

Therefore the required equation is y = -5x + 9

Slope Intercept Form

The slope-intercept form is a way to write the equation of a line.  The equation in a slope-intercept is represented as: 

Slope Intercept – Form : y = mx + b

In the above equation:

  • m is the slope
  • b is y-intercept

Slope: It measures the steepness of the line. The slope of the line can be calculated by measuring the change in y over the change in x.

Y-intercept : It is the point where the line cur across the y-axis. Here the ordered pair is (0,b).

Let us learn to find the equation of a line using the slope-intercept form with the help of an example: You can also solve other interesting examples on this topic by visiting cuemath website.

Example 1: What will be the equation of a line given the slope 5/3 and a y-intercept ( 0,7)?

Solution:

Here, the y-intercept is (0,7) and slope (m) is 5/3

The slope-intercept form equation is given as:

y = mx + b

Placing the values in the slope-intercept form equation, we get

y = 53(x) + 7

53x- y = – 7

Now, we will resolve the above equation by multiplying with 3 on both sides:

3(53x- y) = 3(-7)

5(x – y) = -21

Therefore, the required equation of a line is:  5(x – y) = -21. 

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