Algebra is one of the branches of mathematics that is frequently used in different branches of science. Algebra is a pretty tricky and a tough topic for students. It mainly deals with algebraic expressions and finding the values of unknown variables.
The equation of the line is one of the best techniques used in algebra also known as a linear equation. In this post, we are going to discuss the slope-intercept form along with an explanation and how it is helpful in finding the equation of the straight line.
Table of Contents
What is the slope-intercept form?
A technique used to find the straight-line equation by using different methods is known as the slope-intercept form. It is a frequently used technique as it takes the slope and the y-intercept of the line to find the linear equation of the line.
The general equation of the slope-intercept form is:
Y = m * X + B
Where m is the slope of the line, X & Y are the fixed points of the line, and B is the y-intercept of the line.
For finding the linear equation of the line, you must have sound knowledge of the slope and the y-intercept of the line. let us briefly describe the slope and y-intercept form.
Slope
The slope is the measure of the steepness of the line. It is a widely used method in algebra used for various purposes. Mainly it is very helpful for finding the straight line equation. The slope of the line takes the points of the line for the calculations.
The general formula of the slope is
Slope = m = change in the value of y / change in the values of x
Slope = m = y2 – y1 / x2 – x1
By placing the point of the line, the slope can be calculated easily.
y-intercept
The y-intercept is the point where the graph of the line intercepts with the y-axis. It can be calculated easily by using the slope and points of the line.
By placing the value of the slope and y-intercept of the line, the linear equation of the line can be calculated easily.
Methods of finding linear equations by using the slope-intercept form
There are a few methods of finding the linear equation of the line with the help of the slope-intercept form. Let’s describe the methods briefly.
1. By using two points methods
Two points method is a well-known technique of the slope-intercept form for finding the equation of the line. This method takes the points of the line, finds the slope & y-intercept of the line, and substitutes them in the general equation of the slope-intercept form.
Example
Calculate the linear equation of the line by using two points methods if the points are:
(x1, y1) = (-16, -6) & (x2, y2) = (26, 15).
Solution
Step-1: Take the given points of the line.
x1 = -16, x2 = 26, y1 = -6, y2 = 15
Step-2: Now take the formula of the slope and calculate it with the help of the above points.
m = [y2 – y1] / [x2 – x1]
m = [15 – (-6)] / [26 – (-16)]
m = [15 + 6] / [26 + 16]
m = [21] / [42]
m = 1/2
m = 0.5
Step-3: Now take the general formula of the slope-intercept form.
Y = m * X + B
Step-4: Place the value of the slope, x1, & y1 in the formula of the slope-intercept form to calculate the y-intercept form of the line.
Y = m * X + B
-6 = 0.5 * (-16) + B
-6 = -8 + B
-6 + 8 = B
2 = B
B = 2
Step-5: To calculate the linear equation of the line, place the calculated slope and y-intercept of the line into the equation of the slope-intercept form.
Y = m * X + B
Y = 0.5 * X + 2
Y = 0.5X + 2
The equation of the line can be calculated easily with the help of a y=mx+b calculator.
2. By using the one point and slope method
This is another method of finding the equation of the line. in this method, the slope of the line is given, and a pair of points (x1, y1). You have to calculate the y-intercept of the line with the help of slope and points.
Example
Calculate the linear equation of the line by using the one point and slope method if the points are (12, 18) and the slope of the line “m” is 4.
Solution
Step-1: First of all, take the given information in the line.
Slope of the line = m = 4
Point of the line = (x1, y1) = (12, 18)
Step-2: Now take the general formula of the slope-intercept form.
Y = m * X + B
Step-3: Place the value of the slope, x1, & y1 in the formula of the slope-intercept form to calculate the y-intercept form of the line.
Y = m * X + B
18 = 4 * (12) + B
18 = 48 + B
18 – 48 = B
-30 = B
B = -30
Step-4: To calculate the linear equation of the line, place the calculated slope and y-intercept of the line into the equation of the slope-intercept form.
Y = m * X + B
Y = 4 * X + (-30)
Y = 4X – 30
3. By using the slope and y-intercept method
This is the most frequent method of the slope-intercept form as the slope and y-intercept of the line are given. You have to only substitute the values of the slope and y-intercept in the equation of the slope-intercept form.
Example
Calculate the straight line equation by using the slope and y-intercept method, if the slope of the line is 20 and the y-intercept of the line is -25.
Solution
Step-1: First of all, take the given information in the line.
Slope of the line = m = 20
y-intercept of the line = B = -25
Step-2: Now take the general formula of the slope-intercept form.
Y = m * X + B
Step-3: To calculate the linear equation of the line, place the calculated slope and y-intercept of the line into the equation of the slope-intercept form.
Y = m * X + B
Y = 20 * X + (-25)
Y = 20X – 25
Y = 5(4X – 5)
Final words
Now you can find the equation of the straight line with the help of different techniques of the slope-intercept form. As we have discussed all the basics of the methods with explanations and calculations.