Slope and y-intercept recognize and interpret the y-intercept of a linear function; recognize the constant rate of change in a situation from a verbal.

Slope and y-interceptSlope and y-intercept• recognize and interpret the y-intercept of a linear

function;• recognize the constant rate of change in a situation

from a verbal description, table, graph, or function rule;

• identify proportional and non-proportional linear relationships;

• solve problems involving direct variation;• find the slope of a line from a set of data, or a

graph, function, or verbal description;• look at the effects of m on the parent function when

the value changes;

• interpret slope in a given context.

Essential/Framing QuestionsEssential/Framing Questions

• 1. How can you tell if you’re looking at a positive slope or a negative slope?

• 2. What is the y-intercept of a linear function?

How can we write 7% as a fraction?How can we write 7% as a fraction?

7% as a fraction??7% as a fraction??

• Remember than any percent is a part of 100.

77%

100

The grade of a road is the same as The grade of a road is the same as slopeslope

• Here is the picture:

7 feet

100 feet

Slope of a lineSlope of a line

• The slope measures the “rise” and “run” of the stairs beneath or above the line.

4

4

Slope of a lineSlope of a line

• The “stairs” are all through the line and the same size.

Slope of a lineSlope of a line

• Can I make a line if the stairs aren’t the same size?

Slope of a line (m)Slope of a line (m)

• To find the slope, use the formula

4

4risem

run

Slope of a line (m)Slope of a line (m)

• To find the slope, use the formula

4

441

4m

Slope of a line (m)Slope of a line (m)

• Find the slope of the following lines:

3

2m

1

2A) B)

2

3

risem

run

1

2m

Slope of a line (m)Slope of a line (m)

• Is the slope positive or negative?

Answer:

Positive, Read from left to right

Try for yourselfTry for yourself

• Draw 2 lines with the following slopes on your graph paper.

• A) B)

• Start anywhere on your coordinate plane.

1

2m

3

4m

1

2m

3

4m

Slope of a line (m)Slope of a line (m)

• The last 2 lines had a positive slope, let’s look at slopes with negative slopes

Slope of a line (m)Slope of a line (m)

• We still use rise over run, except the “stairs” are underneath the line.

3

-2

2

3m

Try for yourselfTry for yourself

• Draw 2 lines with the following slopes on your graph paper.

• C) D)

• Start anywhere on your coordinate plane.

1

4m

5

6m

1

4m

5

6m

What do you need to do?What do you need to do?

• Identify the slope on a graph

• First find where the line goes through (intersects the grid lines)

• Draw a triangle and calculate the slope

What do you need to do?What do you need to do?

• Decide if it’s a negative or positive slope

• Trace the triangle on the graph paper

What do you need to do?What do you need to do?

• Use the formula

• Rise is negative 1• Run is 2

risem

run

1

2m

Terrence is teaching his friend Teresa how to ride a skateboard. To help her practice her control of the skateboard, Terrence uses a special drill. As Teresa balances on the board, Terrence pulls the board in a straight line at a steady

rate.Time (seconds) Distance (feet)

0 0.7

1 1.1

2 1.5

3 1.9

4 2.3

5 2.7

6 3.1

7 3.5

8 3.9

9 4.3

• Plot the points on the same coordinate plane

• Describe the way the points look

Do NowDo NowNow, take a look at another situation that can be modeled by a linear function.

The parents of the members of the baseball team want to raise money for new team uniforms. The parents order team baseball caps and sell them at pep rallies and games. They sell the caps for $10 each. They pay a design fee of $100, plus $3.50 for each baseball cap they order from the manufacturer.

Complete these tables to show the money they spend for each cap they order and the money they collect for each

cap they sell

We DoWe DoCreate a graph to represent these data. Then compare your graph with the graph given here.Which amount grows at a faster rate—the amount paid or the amount collected? How do you know?Describe in detail what the graphs of these sets of data look like? How do you know?

modeling (3 minutes)modeling (3 minutes)

Guided PracticeGuided Practice

Guided PracticeGuided Practice

Independent PracticeIndependent Practice

ModelingModeling

Suppose you leave your house and ride your bike to the mall at a steady rate.

You hang out with some friends for a while, and then you realize you have stayed too long

and must hurry home. You ride home at a steady rate, but faster than the rate at which

you rode to the mall. Sketch a graph that represents this situation.

Describe a situation that could be represented by this graph.

ClosureClosureYou have learned about the connections between a constant rate of change, the slope of a

line, and a linear function. Can you solve this puzzle to check your understanding of these

important concepts?

rate of change constant slope linear function

13.When talking about how quickly or slowly a linear function is changing, you are discussing

the function’s ____________.

14.The graph of a ____________ forms a straight line. The line is straight because the

linear function has a _________ rate of change.

15.When you graph a linear function, __________ refers to the steepness of the line the

function makes. The slope of this line is the same as the _________ of the linear

function. The slope can be expressed as a decimal, fraction, or integer.