MSA 1.4 Recognizing Linear Relationships 1) Learning Target: I can determine if a linear relationship is increasing or decreasing. 2) MSA Inv 1 Day 4 Homework: 1) Complete pg. 12 for MSA 1.4 2) Correct online with the EDpuzzle 3) Warm Up: next slide. Be ready to go. It’s a good one!

How much money does Jamal have at the start of camp? Warm Up: Jamal’s parents give him money to spend at camp. Jamal spends the same amount of money on snacks each day. The table shows the amount of money, in dollars, he has left at the end of the day. How much money does Jamal have at the start of camp? How much money does he spend each day? Explain. Is this relationship linear? Is it proportional? Write an equation that represents the relationship. Explain what information the numbers and variables represent. Days 1 2 3 4 5 Money Left $20 $18 $16 $14 $12 $10

Warm Up: Jamal’s parents give him money to spend at camp. Jamal spends the same amount of money on snacks each day. The table shows the amount of money, in dollars, he has left at the end of the day. How much money does Jamal have at the start of camp? How much money does he spend each day? Is this relationship linear? Is it proportional? Write an equation that represents the relationship. Explain what information the numbers and variables represent. Days 1 2 3 4 5 Money Left $20 $18 $16 $14 $12 $10 $20 $2 No. Yes. A constant rate that decreases by $2 each day. It does NOT start at the origin (0,0). y = mx + b y = -2x + 20

discuss and complete p. 10 in the pkt MSA 1.4: Raising Money – Using Linear Relationships As a table group, discuss and complete p. 10 in the pkt

Independent Variable x Dependent Variable y 1. How much money is in the account at the start of the project? Explain $144, (0, 144) 2. How much money is withdrawn from the account each week? $12 3. Suppose the students continue withdrawing the same amount of the money each week. Sketch a graph of this relationship. $144 weeks

amount of money at start $12 withdrawn each week (coefficient or slope) # of weeks (independent variable) y = –12x + 144 y = mx + b amount of money at start (y-intercept) amount of money at end of week (dependent variable) Yes, because the amount of money is decreasing by a constant amount ($12), and it is a straight line.

On your own complete p. 11 in the pkt

The class started with $100. They withdrew $10 per week. Identify 3 things. The class started with $100. They withdrew $10 per week. After 10 weeks the account is out of money.

(constant rate of change) Why is it NOT proportional? This is a linear relationship because the amount of money decreases by $10 every week. (constant rate of change) Why is it NOT proportional? As x increases by 1, y increases or decreases by a constant amount.

y = mx + b y = ─10x + 100 Number of weeks (independent variable) Amount of $ in the account after x weeks (dependent variable) Constant rate of change - $10 (Slope or Coefficient) Amount of money initially in the account

y = mx + b Graph – it will be a straight line Table – as x increases by a constant amount, y increases or decreases by a constant amount Equation y = mx + b Even if … m = 0 (y = x) or b = 0 (y = m) – follows the form:

Both of the relationships in this problem have decreasing rates of change. As the independent variable (x) increases, the dependent variable (y) decreases. These relationships have negative coefficients, so the graph of the line decreases from left to right.

MSA 1.4 Recognizing Linear Relationships Did I reach my Learning Target? I can determine if a linear relationship is increasing or decreasing. 2) MSA Inv 1 Day 4 Homework: 1) Complete pg. 12 for MSA 1.4 2) Correct online with the EDpuzzle

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