A.6 Slope and Slope Intercept Form

Slope

Topics in this quizizz:

- Identifying slope (direction)

- Finding slope of a line (steepness)

- Slope from a Table

- Slope from an Equation

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Multiple Choice

What type of slope?

• positive

• negative

• zero

• undefined

Multiple Choice

What type of slope?

• negative

• steep

• undefined

• zero slope

Multiple Choice

What type of slope?

• zero slope

• undefined

• negative

• positive

Multiple Choice

What type of slope?

• undefined

• positive slope

• negative slope

• zero slope

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• 3

• $$\frac{1}{3}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{5}{3}$$  

• $$\frac{3}{5}$$  

• 5

• $$\frac{5}{4}$$  

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{4}{2}$$  

• 2

• 3

• $$\frac{2}{3}$$  

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{1}{2}$$  

• $$\frac{4}{8}$$  

• 4

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• 3

•   $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

• -3

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

Identify the slope in the equation:

$$y=8x$$  

• 8

• 1/8

• -8

• 0

Multiple Choice

Identify the slope in the equation:

$$y=\frac{5}{6}x$$  

• $$\frac{5}{6}$$  

• $$\frac{6}{5}$$  

• 5

• 6

Open Ended

From what you think or know, what is a slope?

Slope can be expressed in different ways:

What is the slope of a vertical line?

​Constant Rate of change and Steepnness of a line

​​Rate of change=y/x ​

​

The graph shows a change of $94 every 2 weeks, therefore the constant slope is $47 per week.​

Identifying Slope in a Word Problem

Remember that the slope is also the rate of change. So when you are reading a word problem, the slope is rate of change. How is what the problem is talking about changing? You will often see phrases with "per" identifying the slope: per hour, per mile, per day, etc.

Identifying Y-Intercept in a Word Problem

The y-intercept in a word problem is the starting point or starting value. As you read the word problem, ask yourself what are we starting with? That's the y-intercept.

What can you tell me about the graph?

• y-intercept?

• What does it mean?

• rate of change?

Real Life Linear Equations

• y - intercept (0,32)

• These means that the starting fee for renting the car is $32

What can you tell me about the graph?

• y-intercept?

• What does it mean?

• rate of change?

Real Life Linear Equations

• y - intercept (0,32)

• These means that the starting fee for renting the car is $32

Multiple Choice

What is the meaning of the y-intercept of this graph?

• when the gas take is empty

• starting amount of gas

• rate at which the gas take empties

• the starting mileage

The rate of change of this graph

Multiple Choice

Which slope-intercept equation matches the graph?

• $$y=\frac{3}{2}x+2$$

• $$y=\frac{2}{3}x-3$$

• $$y=\frac{2}{3}x+2$$

• $$y=\frac{3}{2}x-3$$

Rate of change (slope)

Multiple Choice

What is the situation of the linear graph?

• The beaker is being filled.

• The beaker is being emptied.

• The beaker is remaining the same amount

Multiple Select

Select ALL statements below that are TRUE.

• slope

  $$-\frac{1}{3}$$

• y-intercept (0,1)

• y-intercept (0,0)

• slope -3

Slope Intercept with Real World Graphs

We are practicing on slope and slope-intercept

Donations

• Tanya has a donation plan of $4 to start and $2 per mile.

• Charlie has a donation plan of $10 to start and $0.50 per mile

Multiple Choice

Which equation represents the total cost of a repair by an electrician after x hours?
An electrician charges $90 per hour plus a $50 travelling fee.

• y = 50 - 90x

• y = 90x + 50

• y = -50x + 90

• y = -90 - 50x

Read your problem and really think about what is happening. Your rate of change will not always be positive.

Multiple Choice

Which equation shows the number of bottles left after x days?
A family buys a case of water with 48 bottles and drinks 5 bottles per day.

• y = 48x + 5

• y = -5 + 48x

• y = -5x - 48

• y = 48 - 5x

Multiple Choice

What is the meaning of the y-intercept of this graph?

• when the gas take is empty

• starting amount of gas

• rate at which the gas take empties

• the starting mileage

Multiple Choice

What is the situation of the linear graph?

• The beaker is being filled.

• The beaker is being emptied.

• The beaker is remaining the same amount

Money Earned Selling Programs

• Ken got a job selling programs.

• He starting payment is $15

• y-intercept (0,15)

• He earns $0.50 per program sold

• slope (rate of change) $0.50 per program

Donations

• Tanya has a donation plan of $4 to start and $2 per mile.

• Charlie has a donation plan of $10 to start and $0.50 per mile

Multiple Choice

Which equation represents this situation: Rocky's Canoe Rental charges a flat fee of $25 and $30 per hour?

• $$y=25x+30$$

• $$y=30x+25$$

• $$y=55x$$

• $$y=30x-25$$

Multiple Choice

Which equation represents this situation:

Pappy's Pizza charges $8 for a plain cheese pizza and $1.50 per topping.

• $$y=1.50x+8$$

• $$y=8x+1.50x$$

• $$y=8x+1.5$$

• $$y=9.50x$$