subject: Slope Linear Equation [print this page] A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line.
In general, the linear equation is given by
ax + by + c = 0 ,
(Source: Wikipedia)
Example Problems to Find Slope of Linear Equation:
Example 1:
Find the slope of the linear equation y = 4x + 13
Solution:
Step 1: Given linear equation
y = 4x + 13 .......................... (1)
Step 2: Slope intercept form of linear equation
y = mx + b ........................... (2)
Step 3: Compare equation (1) and (2)
By comparing the given equation (1) with the slope intercept form(2), we get
m = 4
i.e., slope = 4
Step 4: Solution
The slope of the given linear equation is m = 4
Example 2:
Find the slope of the linear equation 2y = 7x +9
Solution:
Step 1: Given linear equation
2y = 7x + 9 .......................... (1)
Step 2: Slope intercept form of linear equation
y = mx + b ........................... (2)
Step 3: Change the given equation to slope intercept form
2y = 7x + 9
Dividing by 2 on both sides, we get
y = 7/2 x + 9/2 ........................... (3)
Step 3: Compare equation (2) and (3)
By comparing the obtained equation (3) with the slope intercept form(2), we get
m = 7/2
i.e., slope = 7/2
Step 4: Solution
The slope of the given linear equation is m = 7/2
Example 3:
Find the slope of the linear equation 7x + 4y = 11
Solution:
Step 1: Given linear equation
7x + 4y = 11 .......................... (1)
Step 2: Slope intercept form of linear equation
y = mx + b ........................... (2)
Step 3: Change the given equation to slope intercept form
7x + 4y = 11
Subtracting 7x on both sides, we get
4y = - 7x + 11
Dividing by 4 on both sides, we get
y = - 7/4 x + 11/4 ..................... (3)
Step 3: Compare equation (2) and (3)
By comparing the obtained equation (3) with the slope intercept form(2), we get
m = - 7/4
i.e., slope = - 7/4
Step 4: Solution
The slope of the given linear equation is m = - 7/4
Practice Problems to Find Slope of Linear Equation:
1) Find the slope of the linear equation y = 9x + 17
2) Find the slope of the linear equation 3y = 5x +11
3) Find the slope of the linear equation 5x - 6y = 13
