The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.
The Formula
In general, the slope intercept form assumes the formula: y = mx + b.
-
M is the slope
(lesson on slope)
- Mnemonic : 'm' means 'move'
-
B is the y-intercept
(lesson on the y-intercept)
- Mnemonic: 'b' means where the line begins.
Examples
- y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3.
- y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.
Vertical and Horizontal lines
Vertical Lines
The Equation of a vertical line is x = b.
Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b'.
For instance, the red line in the picture below is the graph of the x = 1.
Horizontal Lines
The equation of a horizontal line is y = b where b is the y-intercept.
Since the slope of a horizontal line is 0, the general formula for the standard form equation, y = mx + b becomes y = 0x + b 
y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-intercept. For instance, the red line in the picture below is the graph of the horizontal line y = 1. (In depth lesson on the equation of a horizontal line)
Practice Problems
Problem 1
What is the slope intercept form of the lines graphed below?
Step 2
What is the y-intercept of the line ?
2 or the y value of the point (0, 2).
Step 3
What is the slope-intercept form of this line's equation?
y = mx + b
y = 1x + 2
Problem 2
Look at the picture of the graph below. Find the slope of this line, its y-intercept, then express the equation of this line in slope intercept form.
What is the slope of the line ?
Step 1
What is the y-intercept of the line?
slope = $$ \frac{rise}{run} = \frac{-2}{1} = -2 $$
Step 2
What is the slope intercept form of this line?
-1 which is the y coordinate of the point (0, -1).
Step 3
What is the slope intercept form of the line pictured in the graph below?
The general formula is y = mx + b.
m = slope = -2
b = y-intercept of the line = -1
Therefore, the slope intercept form of this line is y = -2x - 1.
Problem 3
What is the slope intercept form of the line pictured in the graph below?
m = slope of the line = $$ \frac{1}{2} $$
b = y-intercept of the line = 2.
Therefore, the equation of this line in slope intercept form is $$ y = \frac{1}{2} + 2 $$.
Problem 4
What is the slope intercept form of the line pictured in the graph below?
The slope of a horizontal line = 0, because the there is no rise!
Therefore,
- m = 0
- b = y-intercept of the line = 1
Therefore, the equation of this line in slope intercept form is y = 0X + 1 $$ \Rightarrow $$ y = 1.
Practice Problems
Write the slope intercept form for the lines below.
Problem 5
In the general form:
y = mx + b
m = slope = 2
b = the y intercept = 12
The slope intercept form of the equation:
y = 2x + 12
Problem 6
In the general form:
y = mx + b
m = slope = 3
b = the y-intercept = -5
The slope intercept form of the equation:
y = 3x - 5
Problem 7
In the general form:
y = mx + b
m = slope = ½
b = the y intercept = 7
The slope intercept form of the equation:
y = ½x + 7
Linear Equations:
