What is slope intercept form? Defined and explained with examples

What is slope intercept form: In algebra, there are various operations and terms are used to solve and calculate mathematical problems. The equation of the line is the vast method that is used to denote the linear equation of the line.

There are several methods of calculating the linear equation of the line such as x & y-intercept form, slope-intercept form, and point-slope form. In this article, we are going to explain the slope-intercept form along with its definition, techniques, and examples.

Slope intercept form – Definition

In algebra, the slope intercept form is a technique that is used to calculate the linear equation of the line. The linear equation of the line is also known as the equation of the straight line. The y-intercept of the line and the slope of the line are the key factors of the slope-intercept form.

Equation of the slope-intercept form

The general equation of the slope-intercept form is given below.

Y = m * X + B

  • m is the slope of the line.
  • B is the y-intercept of the line.
  • X & Y are the fixed variables of the line.

The knowledge of calculating the y-intercept form and the slope of the line is compulsory for determining the linear equation of the line with the help of the slope intercept form.

Factors of slope intercept form

Let us discuss the factors of slope intercept form that are helpful in calculating the equation of the line.

1.  The slope of the line

The slope of the line is a key factor of the slope intercept form to determine the linear equation of the line. It is the measure of the steepness of the line. It takes the points of the line and calculates the slope using them.

The slope of the line is the quotient of the change in the values of the y-axis and the change in the values of the x-axis. The general expression for calculating the slope of the line is given below.

The slope of the line = m = change in the value of y / change in the values of x

Slope of the line = m = y2 – y1 / x2 – x1

The points of x & y coordinates are evaluated in the above expression to get the slope of the line

2.  The Y-intercept of the line

The point where the line of the graph meets the y-axis of the line is said to be the y-intercept of the line. This factor of the slope intercept form can have calculated by placing the value of the slope of the line and points of the line in the expression of the slope intercept form.

After calculating the slope of the line and the y-intercept of the line, you have to place both the term in the expression of the slope intercept form to get the equation of a straight line.

Techniques of calculating linear equations by using slope intercept form

There are different techniques of calculating the equation of the line with the help of slope intercept form. These techniques are very helpful to ease up the calculation of the linear equation of the line. Let us briefly describe these techniques.

1.  By using a slope intercept form calculator

In this era of development, there are different online tools are created for the sake of helping students to solve their complex educational problems easily.

A slope intercept form calculator is a helpful tool to determine the equation of the line with the help of slope intercept form expression with a single click.

Follow the below steps to find the linear equation of the line by using an online calculator.

  • Select the method i.e., two points, 1 point & slope, or slope & y-intercept.
  • Write the required values.
  • Click the calculate button.
  • The result will come in a couple of seconds.

2.  By using two points technique

In algebra, the technique used to determine the equation of the line by using x and y coordinates points of the line is known as the two points technique. In this technique, first of all, you have to calculate the slope of the line by using coordinate points and then the y-intercept of the line.

Here is an example of two points technique to understand this method more precisely.

Example

Evaluate the equation of the straight line with the help of two points technique of slope intercept form. The coordinates points are:

(x1, y1) = (-6, 7) & (x2, y2) = (18, 15)

Solution

Step-1: First of all, write the given coordinate point of the x & y axis of the line.

x1 = -6

x2 = 18

y1 = 7

y2 = 15

Step-2: Now calculate the slope (m) of the line by placing the coordinate points of the line in the general expression of the slope.  

Slope = m = [y2 – y1] / [x2 – x1]

Slope = m = [15 – 7] / [18 – (-6)]

Slope = m = [15 – 7] / [18 + 6]

Slope = m = [8] / [24]

m = 4/12

m = 1/3

Step-3: Now write the general expression of the slope intercept form.

y = m * x + b … (1)

Step-4: To calculate the y-intercept of the line substitute the calculated value of the slope (m) of the line and the first pair of the line in the expression of the slope intercept form.

y = m * x + b

7 = 1/3 * (-6) + b

7 = -6/3 + b

7 = -2 + b

7 + 2 = b

b = 9

Step-5: Now place the values of the slope of the line and y-intercept of the line in equation (1) to get the linear equation of the line.

y = m * x + b

y = 1/3 * x + 9

y = x/3 + 9

So, y = x/3 + 9 is the equation of the line.

3.  By using the one point and slope technique

According to this technique, you have to calculate the equation of the line with the help of slope and one coordinate pair of points of the line. In this technique, the slope of the line will be given. You have to calculate the y-intercept of the line.

Example

Evaluate the equation of the straight line with the help of 1 point and slope technique, if the slope (m) is equal to 12 and the pair of points are (x1, y1) = (5, -8).

Solution

Step-1: First of all, write the given values to calculate the equation of the line.

Slope of the line = m = 12

Point of the line = (x1, y1) = (5, -8)

Step-2: Now write the general expression of the slope intercept form.

y = m * x + b … (1)

Step-3: To calculate the y-intercept of the line substitute the value of the slope (m) of the line and the first pair of the line in the expression of the slope intercept form.

y = m * x + b

-8 = 12 * (5) + b

-8 = 60 + b

-8 – 60 = + b

-68 = b

Step-4: Now place the values of the slope of the line and y-intercept of the line in equation (1) to get the linear equation of the line.

y = m * x + b

y = 12 * x + (-68)

y = 12 * x – 68

y = 12x – 68

So, y = 12x – 68 is the equation of the line.

4.  By using the slope and y-intercept method

According to this technique, the slope of the line and y-intercept of the line will be given. You have to substitute the values of these terms in the expression of the slope intercept form to calculate the equation of the line.

Example

Evaluate the equation of the straight line with the help of the slope and y-intercept technique, if the y-intercept of the line is equal to -18 and the slope of the line is 9.

Solution

Step-1: First of all, write the given values to calculate the equation of the line.

Slope of the line = m = 20

y-intercept of the line = B = -25

Step-2: Now write the general expression of the slope intercept form.

y = m * x + b … (1)

Step-3: Now place the values of the slope of the line and y-intercept of the line in equation (1) to get the linear equation of the line.

y = m * x + b

y = 9 * x + (-18)

y = 9 * x – 18

y = 9 (x – 2)

So, y = 9 (x – 2) is the linear equation of the straight line.

Wrap up

In this post, we have discussed all the basics of the slope intercept form such as what is it, its expression and techniques to calculate the linear equation of the line, and solved examples. Now you are able to find the linear equation of the line easily.

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