Linear Functions and Graphs

Graphs of Linear Functions

Slope Intercept Form Equation

• y = mx + b

• m is the slope (rate of change; rise/run)

• b is the y-intercept (starting value)

Multiple Choice

Identify the slope as positive, negative, zero or undefined.

• positive

• negative

• zero

• undefined

Multiple Choice

What is the y-intercept of this line: y = 2/3x - 4

• 2/3x

• 3

• 4

• -4

Multiple Choice

What is the slope of this line: y = 6x + 4

• y

• 4

• 6

• 1/6

Graphing using slope intercept form

• Plot the y-intercept on the y-axis

• Determine the slope

• Use the slope to move up (if the slope is positive) or down (if the slope is negative) from the point on the y-axis then to the right.

Multiple Choice

What is the y-intercept of this graph?

• (0,1)
• (0,-2)
• (0,0)
• (0,3)

Multiple Choice

Find the slope and y - intercept

y = 1/2x - 1

• slope: 1/2 y-intercept: -1

• slope: 2 y-intercept: -1

• slope: 1/2x y-intercept: 1

• slope: 2 y-intercept: 5

Multiple Choice

When you graph a line using slope-intercept form (y=mx+b), you graph the ___________ first and then use the ___________ to find the second point.

• origin; slope

• slope; y-intercept

• y-intercept; x-intercept

• y-intercept; slope

Multiple Choice

Which is the graph of y= -x + 2?

• A
• B
• C
• D

Writing Equations from graphs

• Identify the y-intercept (where the line crosses the y-axis)

• Determine the slope (rise/run - how you have to move to get from one point on the line to another)

• Plug in the slope for m, the y-intercept for b in y=mx+b

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

Multiple Choice

Which equation matches the graph? (Click me to see the image)

• y = 2x

• y = 1/4 x + 2

• y = 1x + 4

• y = -2x

Multiple Choice

Write the equation of the line.

• y= -1x-3

• y= -3x-1

• y=-1/3x-1

• y= -3x-3

Writing equations from key information

• Always start with y = mx + b

• If you know the slope and y-intercept, plug in for m and b

• If you only know the slope and a point, plug in the slope and the x and y values to solve for b

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3

• y=2/3-3

• y=2/3x-3

• y=2/3x+3

Multiple Choice

What is the equation of the line that has a slope of 5 and goes through the point (2,7)?

• y = 5x + 3

• y = 1/5x - 3

• y = 1/5x + 3

• y = 5x - 3

Multiple Choice

What is the equation of the line passing through points (1,1) and (3,-5).

• y = -3x + 4

• y = 3x - 4

• y = -3x - 4

• y = 3x + 4

Converting to slope-intercept form

• Step 1: distribute if you see parentheses

• Step 2: combine like terms

• Step 3: isolate y

• Step 4: write in the form y=mx+b

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = -2(x + 4)

• y=2x-5

• y=-2x+7

• y=-2x-5

• y=-2x +1

Multiple Choice

What is the first step to convert this equation into slope-intercept form?
$$y+4=-9\left(x+3\right)$$  

• Subtract 4 from both sides of the equation

• Add 4 to both sides of the equation

• Distribute -9 to everything in the parentheses

• Distribute 9 to everything in the parentheses

Multiple Choice

Which equation represents 4x - 2y = 6 in slope intercept form.

• y = 2x - 3

• y = -2x + 3

• 
  

  $$y\ =\ \frac{1}{2}x\ -\ 3$$

• y = 2x + 8

Linear vs. Non-linear

• Linear functions form a straight line and have a constant increase or decrease of y as x increases or decreases

• Non-linear functions do not form a straight line and as x increases, y does not increase at a constant rate

Multiple Choice

$$y\ =\ 6x\ +\ 5$$  

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear