# What is a slope-intercept form?

### The equation of the straight line can be calculated easily by using the equation of the slope intercept form. Follow the below steps to measure the linear equation of the line.

• Identify the given points of the line.
• Find the slope of the line by using the given points.
• Use the calculated slope and a pair of numbers to calculate the y-intercept of the line.
• Substitute the terms of slope and y-intercept in the general formula of the slope intercept form.
• The result will be the linear equation of the line.

You can also use a slope intercept form calculator to get the step by step solution in a couple of seconds. Follow the below steps to calculate the linear equation of the line using this tool.

Step 1: First of all, select the input option i.e., two points, one point, and slope, or y-intercept and the slope.
I Have :
Step 2 : Input the given value.

I Have :

Step 3 : Hit the calculate button to get the result.

Step 4: The result with the steps will show below the calculate button.

RESULT

Slope Intercept Form
Let us take some examples to learn how to calculate the equation of the line.

• Example 1: For positive integers
Find the equation of the straight line of (13, 21) and (10, 23) by using a slope-intercept form.
Solution-
Step 1: First of all, identify the given points.

x1 = 21, x2 = 23, y1 = 13, y2 = 10

Step 2: Find the slope of the line by using the given points.

Slope of the line,

m = 𝚫y/ 𝚫x

m = y2 – y1/ x2 – x1
m = (10 – (13)) / (23 – 21)
m = (10 – 13) / (23 – 21)
m = (– 3) / (2)
m = – 3 / 2
m = -1.5

Step 3: Write the general formula of the slop-intercept form.

y = mx + b

Step 4: Put the calculated slope in the formula of the slope intercept form.

y = mx + b

y = -1.5x + 40.5

• Example 2: For negative integers
Find the equation of the straight line of (-3, -1) and (-20, -21) by using a slope-intercept form.

Solution
Step 1: First of all, identify the given points.

x1 = -3, x2 = -20, y1 = -1, y2 = -21

Step 2: Find the slope of the line by using the given points.
Slope of the line,

m = 𝚫y/ 𝚫x
m = y2 – y1/ x2 – x1
m = (-21 – (-1)) / (-20 – (-3))
m = (-21 + 1) / (-20 + 3)
m = (-20) / (-17)
m = 20 / 17
m = 1.1765

Step 3: Write the general formula of the slop-intercept form.
y = mx + b

Step 4: Put the calculated slope in the formula of slope intercept form.

y = mx + b
y = 1.1765x + b
Step 5:
Find the y intercept of the slope-intercept form by putting any pair of points and slope of lines.
y = 1.1765x + b
-1 = 1.1765(-3) + b
-1 = -3.5295 + b
-1 + 3.5295 = b
2.5295 = b
y-intercept = b = 2.5295

Step 6: Substitute the calculated values in the formula of the slope-intercept form.
y = mx + b
y = 1.1765x + 2.5295

Summary
In algebra, the slope-intercept form is the most frequently used method to express the linear equation of the line. in this article, we have discussed all the basics of this method. Now you can solve any problem easily related to the slope.

A note from the author:

I'm a mathematician. I'm writing the articles for the kids and grade 11 & 12 students. I write mostly on the various topics of calculus & algebra like derivative, integral, slope, slope intercept form, limits, etc.
I am a sophomore psych major at Case Western Reserve University. In the future, I plan on researching influence to help people improve their lives. I'm a senior psychology student with a minor in marketing at Case Western Reserve University. In the past, I've interned for a number of nonprofits and for-profit organizations, including a collaboration between Paragon One and Meta, formerly known as Facebook. I like walking around outdoors, exploring new places, and creating personalized greeting cards. I am a 3rd year college student studying cognitive science and minoring in marketing. I love learning about how the human brain works, and applying my knowledge of cognitive science and marketing to help improve the lives of others.