Slope Intercept Equation of a Line

y = mx + b

m is the slope of the line.

b is where the line crosses the y-axis.  This point can be represented by the ordered pair (0,b) because at the y-axis the value of x is zero.

Example:

Given the equation y = 3x + 7

The slope is 3 or 3/1 which means that as the line progresses from left to right it will go up 3 units for each unit it moves to the right.

The line will cross the y-axis at (0,7)

To evaluate the equation where x = 7, simply replace the x in the equation with a 7 and simplify as shown below.

y = 3x + 7

y = 3(7) + 7

y = 21 + 7

y = 28

Therefore the point (7,28) is on the line.

To evaluate the equation where x = 8, simply replace the x in the equation with an 8 and simplify as shown below.

y = 3x + 7

y = 3(8) + 7

y = 24 + 7

y = 31

Therefore the point (8,31) is on the line.

Note that since the slope is 3, as the line goes from where x = 7 to where x = 8 the value of y went from y = 28 to y = 31, which is an increase of 3, which is the slope.

This equation can be solved for 'b' as shown below.

y = mx + b  Turn equation around

mx + b = y  Subtract mx from each side

mx - mx + b = y - mx  but since mx - mx is zero then

b = y - mx

This equation can also be solved for 'x' as shown below.

y = mx + b  Turn equation around

mx + b = y  Subtract a 'b' from each side

mx + b - b = y - b but since b - b = zero then

mx = y - b   Next divide both sides by 'm'

mx/m = y/m - b/m  Reduce the mx/m to just x

x = y/m - b/m

 

This equation can also be solved for 'm' as shown below.

y = mx + b  Turn equation around

mx + b = y  Subtract a 'b' from each side

mx + b - b = y - b but since b - b = zero then

mx = y - b   Next divide both sides by 'x'

mx/x = y/x - b/x  Reduce the mx/x to just m

m = y/x - b/x