An equation is called a linear equation because all the solutions for this equation always result in a Straight Line. So the Linear Equations have only individual variables (never consist of product of variables). If any equation consisting of term having power other than 1 such that 2x$^2$+ 3, x$^2$/2, xy, x+y$^2 $etc. are known as non linear equations.

How to Find Slope from an Equation

The general form of linear equation is: ax + by + c = 0,
Here in above equation ‘a’ and ‘b’ are coefficients of ‘x’ and ‘y’ respectively and are not equals to zero.

We must pick two x’s and then solve for every corresponding value of ‘y’ i.e. if we pick x = 3 then we will place this in the above equation and will find out the value of ‘y’; similarly we may pick many values for x and then find out the corresponding value of ‘y’.

For finding the Slope of a linear equation we must use a formula that is, m = $\frac{y_2-y_1}{x_2-x_1}$ this means that we need at least two points on the line.
We may also change the order of subtraction then the formula become, m = $\frac{y_1-y_2}{x_1-x_2}$ this means that the order of subtraction does not matter; the only thing which matters is that the order of subtraction of ‘y’ values must be same as the order of subtraction of ‘x’ values. 

In mathematics, if we want to find the Slope of a line that passes through two points $(x_1, y_1)$ and $(x_2,y_2)$ then there is a formula for Slope which is,
Slope = m = $\frac{y_2-y_1}{x_2-x_1}$
How do you find the slope of the line if the equation is in standard form? If line of equation in the form y = mx + c where m is the slope of line , then m = 1/x(y - c) is the formula for the slope of line.


Example 1 : Find the slope of a line if line passes through two points: (1, 4) and  (5, 3).
We know, the slope formula is;  m = $\frac{y_2-y_1}{x_2-x_1}$
So by putting the values of co-ordinates: $(x_1,y_1)$ = (1, 4) and  $(x_2,y_2 )$ = (5, 3)
m = $\frac{3-4}{5-1}$
m = -1/4.
So the slope of a line is -1/4.

Example 2 :  If we talk about slope according to Algebra and we have a linear equation which have a slope than formulate linear equation in terms of slope, y = mx + b. Calculate the intercept of y. (Consider line passing through the point (1, 2) and slope is 5.)
Rewrite the equation as:
b = y - mx,
Since point (1, 2) lies on the line, and m = 5, we get
b = 2 - 5(1)
b = 2-5 = -3
And therefore the value of b = -3.
Here ‘b’ is also the y- axis intercept which is the value of ‘y’. 

Example 3: Write the equation of a line which passes through the co-ordinate (7, 5) and the slope of that line is 9.

Solution: According to the slope formula equation,
y = mx + b
or b = y - mx,
Given: x = 7, y = 5 and m = 9
b = 5 - 9 ( 7)
b = - 58,
By putting the value of ‘b’ in standard form of linear slope equation.
y = 9x - 58.

Example 4: Find the slope of a line 2x - 3y = 9.
Solution: Write the given equation in the slope intercept form
2x - 3y = 9,
-3y = -2x + 9,
y = (2/3)x - 3
Above equation is similar to y = mx + c. After comparing we have, m = 2/3

Example 5: Find the equation of a line which is parallel to another line having slope 2/3 and passes through points (4, -1).
Solution: Now according to formula of line which has a slope ‘m’ and passes through Point (x$_1$, y$_1$) is,
y - y$_1$ = m (x - x$_1$),
Putting the values of co-ordinates ((x$_1$, y$_1$) which is (4, -1) and slope m=2/3 in the above formula
y - (-1) = 2/3  (x - 4),
y + 1 = (2/3)x - 8/3
y = (2/3)x - 8/3 - 1
y = (2/3)x - 11/3
So the parallel lines which have a parallel slope 2/3 and passes through points (4, -1) is
y = (2/3)x - (11/3)
(since parallel lines have the same slope)

Practice Problems

Problem 1: Write the equation of a line which passes through the co-ordinate (10, 2) and the slope of that line is 11.
Problem 2: Find the slope of a line passes through the lines (11, 2) and (10, 5).
Problem 3: Find the slope of a line 2x - 3y = 9.
Problem 4: Find the equation of a line having slope -3 and passes through points (3, -2).