1. LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM Common Core State Standards:
Section 2.3
LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM
Common Core State Standards:
MACC.912.F-IF.B.6: Calculate and interpret the average rate of change
of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
MACC.912.F-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
MACC.912.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2. RATE YOUR UNDERSTANDING
LINEAR FUNCTIONS AND SLOPE- INTERCEPT FORM
MACC.912.F-IF.B.6: Calculate and interpret the average rate of change
of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
MACC.912.F-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
MACC.912.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
RATING
LEARNING SCALE 4
I am able to
write a linear equation in real world situations in slope-intercept and use the model to make predictions 3
find the slope
write and graph linear equations using slope-intercept form 2
find the slope with help
write and graph linear equations using slope-intercept form with help 1
understand the components of slope-intercept form
TARGET

3. WARM UP
Tell whether the given ordered pair is a solution of the equation.
1) 4y + 2x = 3; (0, 0.75) 2) y = 6x – 2; (0, 2)
Yes No

4. KEY CONCEPTS AND VOCABULARY
Rate of Change – a ratio that shows the relationship, on average, between two changing quantities
Slope is used to describe a rate of change. Because a linear function has a constant rate of change, any two points can be used to find the slope.
RATE OF CHANGE
POSITIVE
NEGATIVE
ZERO
UNDEFINED

5. EXAMPLE 1: DETERMINING A CONSTANT RATE OF CHANGE
Determine the rate of change. Determine if the function is linear. Justify your answer.
a) b) x y 1 4 5 6 9 8 13 10 17 12 x y 1 2 3 6 4 8 5 12
Linear;
Rate of Change between all points is 1/2
Non-Linear;
Rate of Change varies between 2 and 4

6. EXAMPLE 2: FINDING THE SLOPE USING A GRAPH
Find the slope of each line.
a) b) c)
3/4 –2

7. EXAMPLE 3: IDENTIFYING SLOPES
Label the slopes of the lines below (positive, negative, etc.).
Undefined
Negative
Negative
Zero
Positive

8. EXAMPLE 4: FINDING SLOPES USING POINTS
Find the slope of the line through the given points.
(3, 2) and (4, 8)
(2, 7) and (8, –6) c) 6 3

9. KEY CONCEPTS AND VOCABULARY
SLOPE-INTERCEPT FORM
y = mx + b
m = slope; (0, b) = y-intercept
Steps for Graphing a Linear Function
(Slope-Intercept Form)
Identify and plot the y-intercept
Use the slope to plot an additional point (Rise/Run)
Draw a line through the two points

10. EXAMPLE 5: WRITING AND GRAPHING LINEAR EQUATIONS GIVEN A Y-INTERCEPT AND A SLOPE
Write an equation of a line with the given slope and y-intercept. Then graph the equation.
slope of 1/5 and b) slope of –2
y-intercept is (0, –3) and y-intercept is (0, 7)

11. EXAMPLE 6: GRAPHING LINEAR EQUATIONS
Graph the linear equation.
a) b)

12. EXAMPLE 7: WRITING A LINEAR EQUATION IN SLOPE-INTERCEPT FORM
What is the equation of the line in slope-intercept form?
a) b)

13. EXAMPLE 8: FINDING THE Y-INTERCEPT GIVEN TWO POINTS
In slope-intercept form, write an equation of the line through the given points.
a) (4, –3) and (5, –1) b) (3, 0) and (–3, 2)

14. EXAMPLE 9:USING LINEAR EQUATIONS IN A REAL WORLD SITUATION
To buy a $1200 stereo, you pay a $200 deposit and then make weekly payments according to the equation: a = 1000 – 40t, where a is the amount you owe and t is the number of weeks.
How much do you owe originally on layaway?
What is your weekly payment?
Graph the model.
$1000
$40

16. Parallel lines Perpendicular lines

17. Write an equation of a line:
Given a point (-2,1) on the line and the equation of a line Parallel to it 𝑦 = −3𝑥 +1
Given a point (2,2) on the line and the equation of a line Perpendicular to it 𝑦 = −3/5 𝑥 +2

18. Common Core State Standards:
Section 2.2
DIRECT VARIATION
Common Core State Standards:
MACC.912.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

19. RATE YOUR UNDERSTANDING
DIRECT VARIATION
MACC.912.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
RATING
LEARNING SCALE 4
I am able to
write and solve an equation of a direct variation in real-world situations or more challenging problems that I have never previously attempted 3
write and graph an equation of a direct variation 2
write and graph an equation of a direct variation with help 1
understand the definition of direct variation
TARGET

20. WARM UP
Solve each equation for y. 1) 2) 3)

21. KEY CONCEPTS AND VOCABULARY
Direct Variation - a linear function defined by an equation of the form y=kx, where k ≠ 0.
Constant of Variation - k, where k = y/x
GRAPHS OF DIRECT VARIATIONS
The graph of a direct variation equation y = kx is a line with the following properties:
The line passes through (0, 0)
The slope of the line is k.

22. EXAMPLE 1: IDENTIFYING A DIRECT VARIATION
For each function, tell whether y varies directly with x. If so, find the constant of variation.
a) 3y = 7x b) 5x = –2y No
Yes;

23. EXAMPLE 2: FINDING THE CONSTANT OF VARIATION
Determine if each graph has direct variation. If does, identify the constant of variation.
a) b) c) No
Yes;
Yes;

24. EXAMPLE 3: WRITING A DIRECT VARIATION EQUATION
Suppose y varies directly with x, and y = 15 when x = 27. Write the function that models the variation. Find y when x = 18.

25. EXAMPLE 4: WRITING A DIRECT VARIATION FROM DATA
For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation.
a) b) x y -1 3 2 -6 5 15 x y 7 14 9 18
– 4
– 8 No
Yes; k = 2, y = 2x

26. EXAMPLE 5: USING DIRECT VARIATION IN REAL-WORLD SITUATIONS
Weight on the moon y varies directly with weight on Earth x. A person who weighs 100lbs on Earth weighs 16.6lbs on the moon. What is an equation that relates weight on Earth x and weight on the moon y? How much will a 150lb person weigh on the moon?