Slope Intercept Form

Slope Intercept Equation of vertical and horizontal lines

• Vertical Lines
  
  

  The Equation of a vetical 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 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.
  

Interactive Slope Intercept Form

Try interactive Line below to explore the slope intercept form of a line

What is the slope intercept form of the line below?

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

slope = rise/run 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 of Line  
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 = rise/run = -2/1

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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 = ½
b= y-intercept of the line = 2

Therefore, the equation of this line in slope intercept form is y = ½X + 2

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

 answer 

The slope of a horiztonal 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

Directions: For all questions below, express your answers using slope intercept form.

Write the equation of a line that has a slope of ½ and that goes through the point (2,3).
 answer 

y = ½x + b	Goal: Find "b", the y-intercept
3 = ½(2)+ b	Step 1: substitute in the point (2,3)
3 = 1 + b 3 - 1 = 2 = b	Step 2: solve equation for b
y = ½x +2	Last Step: Insert b into equation

Below is graph of y = ½x +2

If the slope of a line is 10 and the line goes through the point (3, 34), express the equation of this line in slope-intercept form.
 answer 

If the slope of a line is 3 and the line goes through the point (6,23), express the equation of this line in slope-intercept form.
 answer 

y =  3x + b

23 = 3 × 6 +b   23 = 18 + b

23 - 18 = b = 5

y = 3x + 5

If the slope of a line is 0 and the line goes through the point (7,5), express the equation of this line in slope-intercept form.
 answer 

There are two ways to approach this problem. First, you can look at this as a horizontal line, any horizontal line has the standard form equation of y = b where b is the y intercept. Since the slope is 0, and only horizontal lines have a slope of zero, all points on this line including the y-intercept must have the same y value. This y-value is 5, which we can get from the fact that the line passes through the point (7,5). Therefore the standard form equation of this horizontal line is y = 5.

y =  0x + b	1) Plug slope into M
5= 0 • 7 + b   5 = b	2) Substitute x and y coordinates of point
b = 5	3) Solve equation for B
y = 0x + 5 y = 5	4) Plug in B as the y-intercept and write standard form equation.

If the slope of a line is undefined and line goes through the point (-3, -13), express the equation of this line in slope-intercept form.
 answer 

Since the slope is undefined, the line is a vertical line. Therefore, the equation is just x = -3.