Slope Intercept Form

Video Tutorial on Slope Intercept Form

The Formula

In general, the slope intercept form assumes the formula: y= mx +b.

• m = slope of the line
  • mnemonic : 'm' means 'move'
• b = 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 .

Slope Intercept Equation of 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)

Step 1) What is the slope of the line below?

Answer

slope = $$ \frac{rise}{run} =\frac{1}{1} =1

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Step 2) What is the y-intercept of the line on the left?

Answer

2 or the y value of the point (0,2)

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Step 3) What is the slope-intercept form of this line's equation?

Slope Intercept Form

y=mx+b
y = 1x + 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 on the left?

Answer

slope =$$ \frac{rise}{run} = \frac{-2}{1} = -2$$

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What is the y-intercept of the line on the left?

Answer

-1 which is the y coordinate of the point (0, -1)
What is the slope intercept form of this line?

Answer

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



What is the slope intercept form of the line pictured in the graph below?

Answer

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 $$y = \frac{1}{2} +2 $$


What is the slope intercept form of the line pictured in the graph below?

Answer

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 y = 1

Problem 1) A line with a slope of 2 and a y-intercept of 12

Answer

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 2) A line with a slope of 3 and a y-intercept of -5

Answer

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 3) A line with a slope of ½ and a y-intercept of 7

Answer

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