Moving Straight Ahead Investigation 1.3 Using Linear Relationships Learning Target: I can examine the pattern of change in a linear relationship. Homework: 1) Complete pg. 9 for MSA 1.3 2) Correct online with the Zaption Review video. Warm Up: Find the unit rate and use it to write an equation relating the two quantities: a)200 dollars for 50 t-shirts b)70 dollars to rent 14 video games c)12 tablespoons of sugar in 3 glasses of Cola y = mx

Warm Up: Find the unit rate and use it to write an equation relating the two quantities: a)200 dollars for 50 t-shirts b)70 dollars to rent 14 video games c)12 tablespoons of sugar in 3 glasses of Cola $ shirts = X 1 shirt x = $4 per shirt 200 = 4(50) y = mx $70 14 videos = X 1 video x = $5 per video 70 = 5(14) 12T. 3 glasses = X 1 glass x = 4T. per glass of Cola 12 = 4(3)

Add Dependent Variable and Independent Variable to your Vocabulary Toolkit a dependent variable? an independent variable? 200 dollars for 50 t-shirts 200 = 4(50) What is WARM UP: The total amount spent ($150) is dependent upon the number of t-shirts at $4 each 70 dollars to rent 14 video games 70 = 5(14) The total amount spent ($70) is dependent upon the number of video games rented at $5 each The total tablespoons of sugar (12T.) is dependent upon the number of glasses of Cola at 4T. of sugar each 12 T. of sugar in 3 glasses of Cola 12 = 6(3)

y = mx + b dependent variable independent variable slope constant rate of change rate of change coefficient y-intercept

The class refers to these as pledge plans. Tables, graphs, and equations will help predict how much money might be raised with each plan.

Independent Variable Distance = X Dependent Variable $ = y Make a table for each student’s pledge plan. Show the amount of money each of his or her sponsors would donate if he or she walked distances from 0 to 6 kilometers. What are the dependent (y) and the independent (x) variables?

Independent Variable Distance = x Dependent Variable $ = y For each pledge plan, what pattern of change between the two variables do you observe in the table? In other words: As x goes up by 1, what happens to y? Alana: as (x) increases by 1 km, (y) increases by $0.50 Gilberto: as (x) increases by 1 km, (y) increases by $2 Leanne: as (x) increases by 1 km, (y) has no change

Independent Variable Distance = X Dependent Variable $ = Y FYI: (For Your Information) What is the starting point for each student? This is also called the y-intercept. What is the rate of change for each student? This is also called the slope.

B. Graph the three pledge plans on the same coordinate axes. Use a different color for each plan. dependent variable independent variable x-axis y-axis KEY Alana Gilberto Leanne

For each pledge plan, what pattern of change between the two variables do you observe in the graph? dependent variable independent variable x-axis y-axis In other words: As x goes up by 1, what happens to y? Alana’s rate starts at $5 and increases with each km walked. Gilberto’s rate starts at $0 and increases at a much faster rate than Alana. Leanne starts at $10 and the rate doesn’t change.

FYI: (For Your Information) What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6,12) represent? Whose line is it on? Whose line are these points on? (10,10) (6,8) FYI: (For Your Information) What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6,12) represent? Whose line is it on? Whose line are these points on? (10,10) (6,8) Gilberto Alana

Alana: y = 0.50x + 5 Gilberto: y = 2x or y = 2x + 0 Leanne: y = 0x + 10 or y = 10 y = money earned in dollars (dependent variable) x = distance walked in km (independent variable) The coefficient (the number in front of the variable) represents the walking rate. y = money earned in dollars (dependent variable) x = distance walked in km (independent variable) The coefficient (the number in front of the variable) represents the walking rate. y = mx C. For each pledge plan, write an equation that represents the relationship between the distance walked and the amount of money donated. Explain what information each number and variable in the equations represents.

The pattern of change is the coefficient of x Alana: y = 0.50x + 5 Gilberto: y = 2x Leanne: y = 0x + 10 For each pledge plan, what pattern of change between the two variables do you observe in the equation? (the walking rate) (the independent variable)

The relationship between money and distance walked for… Gilberto is proportional! It is NOT proportional for Leanne and Alana because sponsors donate an initial amount in addition to money donated per kilometer. This makes the ratio of money donated to kilometers walked not a constant. D. Does each pledge plan represent a proportional relationship? Alana: y = 0.50x + 5 Gilberto: y = 2x or y = 2x + 0 Leanne: y = 0x + 10 or y = 10

In a table: as x increases by 1, y changes by a constant amount In a graph: there is a straight line In an equation: it follows the formula of y = mx + b E. How can you determine if a relationship is linear from a table, a graph, or an equation?

MSA 1.3 Walking Rates & Linear Relationships Did I reach my Learning Target? I can examine the pattern of change in a linear relationship. Homework: 1) Complete pg. 9 for MSA 1.3 2) Correct online with the Zaption Review video.

Alana: $ (8km) = $9 Gilberto: $2(8km) = $16 Leanne: $10 per sponsor no matter how far she walks MSA 1.3 HOMEWORK:

Alana: $ (?km) = $10, so 0.5 x 10 km = 5 Gilberto: $2 x ? km = $10, so 10/2 = 5 km Leanne: Can’t determine!

(12, 11) lies on Alana’s graph. If Alana walks 12km, each sponsor donates $11. When her distance is zero, she already has $5 (0, 5) it is the starting point, or y-intercept! 5 is the term added to 0.5x

y = 2x – $4.75 Amount of $ Gilberto raises from each sponsor after he has paid for the T-shirt. Constant rate of change $2 Amount subtracted for each t-shirt km walked y = mx + b

This graph starts at (0, -4.75), the other was (0,0) Both graphs have the same steepness (slope). For every value of x, the y-coordinate of a point on this graph is exactly 4.75 less than the y-coordinate on the other graph. Yes, it is linear. There is a constant rate of change, and it is a straight line.