Slope intercept form

Linear Functions

What do you think a linear function is?

Linear Functions

A linear function is a rule described by a linear equation. The rate of change is constant, and the graph of the equation is a line.

You put something in, you get something out

• The function takes in a number, applies a rule to it, and spits out another number

It does the same thing every time

• The machine/function applies the same rule to every input every time, and it does it without changing the output

• Example: y = 2x

For every input, you can only get 1 output

• One input cannot have two or more different outputs

Functions

• You put a number into your machine, it does something to that number and it gives you the new number

• It does the same thing every time

• For every input, you can get only one output

• Everything we do in math is functions

Two inputs can have the same output

The important thing is there is only one output PER input

Does this table represent a linear function? Why?

Multiple Choice

Is the graph linear or nonlinear?

• It's linear because it's a straight line.

• It's nonlinear because it's going up.

• It's linear because it's going up.

• It's nonlinear because it's not a straight line.

Multiple Choice

Is the graph linear or nonlinear?

• It's linear because it's a straight line.

• It's nonlinear because it's going both up and down.

• It's nonlinear because it's not a straight line.

• It's linear because I like the shape.

Multiple Choice

Is the graph linear or nonlinear?

• It's nonlinear because the line is red.

• It's nonlinear because it goes both up and down.

• It's nonlinear because it's a U shape.

• It's nonlinear because it's not a straight line.

Multiple Choice

Is the graph linear or nonlinear?

• It's linear because it's going down.

• It's linear because it's a straight line.

• It's nonlinear because it's going down.

• It's nonlinear because it's not a straight line.

Multiple Choice

Is the graph linear or nonlinear?

• It's linear because it's a straight line.

• It's nonlinear because it goes both up and down.

• It's linear because it's a V shape.

• It's nonlinear because it's not a straight line.

Multiple Choice

Is the equation linear or nonlinear? $$y=-3x^2-7$$

• It's nonlinear because there are exponents.

• It's nonlinear because there are negative numbers.

• It's linear because it's written as y =

• It's linear because there is a slope.

Multiple Choice

Is the equation linear or nonlinear? $$y=\frac{3}{4}x-5$$

• It's linear because the y-intercept is negative.

• It's nonlinear because the y-intercept is negative.

• It's linear because there are no exponents.

• It's linear because the slope is positive.

Multiple Choice

Is the equation linear or nonlinear? $$y=\frac{4}{x}-7$$

• It's linear because it's written as y =

• It's nonlinear because there is an "x" as a denominator.

• It's linear because the slope is positive.

• It's nonlinear because the y-intercept is negative.

Multiple Choice

Is the equation linear or nonlinear? $$y=\frac{x}{4}+8$$

• It's linear because it graphs as a straight line.

• It's linear because the number are all positive.

• It's nonlinear there is a fraction.

• It's nonlinear because there are only even numbers in the problem.

Multiple Choice

which of the following is a linear Function?

Multiple Choice

Is the function linear or nonlinear?

• Linear Function
• Nonlinear Function

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

What is the slope of this line?

m=rise/run

• m = 1/2

• m = 2/1

• m = -2/1

• m = -1

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Slope and Y-Intercept of a Graph

​

Slope of a Graph using Rise over Run

You can find the slope of a graph using rise/run

Open Ended

What is a strategy you can use to find the slope of a graph?

Let's slow it down...

I recognize that there was a lot of information thrown at you during our lesson yesterday! Let's slow it down and take it step by step.

Today you will be reviewing two concepts:

1. Finding the slope and y-intercept from a graph

2. Finding the slope and y-intercept from an equation

By the end of this Quizizz, my hope is that we will feel more confident in these concepts!

1. Identify Slope and the Y-Intercept...

From a GRAPH!

Please watch the video on the next slide to refresh your memory!

(4 minutes)

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

Find the slope

• 5/2
• -5/2
• 2/5
• -2/5

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Multiple Choice

Find the slope of the line that passes through
(10, 1) and (5, 2)

• 1/5
• -1/5
• 5
• -5

2. Identify Slope and the Y-Intercept...

From an EQUATION!

Y-Intercept of a Graph

The y-intercept is the point where the line crosses the y-axis

Please watch the video on the next slide to refresh your memory!

(4 min)

Please watch the video on the next slide to refresh your memory!

(4 minutes)

Multiple Choice

What is the y-intercept of the line?

• (0, -4.5)
• (0, 4.5)
• (0, 5)
• (0, -5)

Multiple Choice

What is the y-intercept of the line?

• (0, 4)
• (0, -4)
• (0, 5)
• (0, -5)

Multiple Choice

What is the y-intercept of this graph?

• b = -2

• b = 2

• b = 1

• b = -1

Multiple Choice

What is the y-intercept of the line?

• (0, 2)
• (0, -2)
• (0, 1)
• (0, -1)

Multiple Choice

• Linear Function
• Nonlinear Function

Multiple Choice

What is the y-intercept of the graph shown?

• -2

• 4

• 2

• -4

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Multiple Choice

What is the y-intercept of the graph shown?

• 2

• -3

• $$\frac{1}{2}$$

• 3

Multiple Choice

What is the y-intercept of this graph?

• -1
• 3
• -3
• -2

Multiple Choice

What is the y-intercept of this graph?

• 4
• -2
• 2
• 1

Multiple Choice

What is the y-intercept of the graph?

• -2

• -3

• -4

• -5

Multiple Choice

What is the y-intercept of this graph?

• 2

• 3

• 4

• 5

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope
• y-intercept
• linear
• point-slope

Multiple Choice

What does 'b" represent in y=mx+b

• y-intercept
• macaroni
• nothing
• slope

Multiple Choice

In the equation $$y=-3x+1$$  

1 is the ______.

• slope

• y-intercept

Multiple Choice

In the equation $$y=\frac{1}{3}x-2$$  , the is the

$$\frac{1}{3}$$  is the ______.

• slope

• y-intercept

Multiple Choice

In this equation, what is the y-intercept?
y= 4x - 7

• 4
• -7
• 7
• -4

Multiple Choice

Which equation has a slope of 8 and a y-intercept of 2?

• y = 2x + 8

• y = 2x - 8

• y = 8x - 2

• y = 8x + 2

Multiple Choice

What is the y-intercept of the equation below?

y = x - 4

• 4

• -4

• 1

• 0

Multiple Choice

Identify the slope and the y-intercept in y = 6x + 2

• slope = 2, y-intercept = 6

• slope = 6, y- intercept = 2

• slope = 0, y- intercept = 2

• slope = 6, y- intercept = 0

Lesson 2: Graphing Slope-Intercept Form

Graphing a linear relationship from slope-intercept form equation

y = mx + b

• What does the equation give us so that we can graph the line?

• 
  

• m = __________

• b =  __________

• Graph the line

y = -x + 2

• m = ___________

• b = ____________

• Graph the line

y = 4

• m = ____________

• b = _____________

• Graph the line

x = 5

• m = ________________

• b = _________________

• Graph the line