Start with 2 gallons of water in the pool 8WB Your group task is to build a set of stairs and a handicap ramp at the side. How are the problems similar? Identify the rate of change and initial value of a linear relationship in the table, graph, equation, context, and geometric model of a linear pattern. Find the unit rate for this proportional relationship. The exchange rate of Euros to Dollars is a proportional relationship.

Stage 4 has 9 blocks. How much will it cost Padma to buy the 5 pounds of candy that she needs? Fill in the missing items in the table if x represents the number of hours that have passed since Doug began pouring concrete and y represents the amount of concrete poured Time elapsed hours x Amount of concrete poured square feet y Also, ask them why is the first quadrant only included for this graph. If you want to describe the change in elevation per mile and the x values in this table are changing by 2 the difference in the y values must be cut in half.

Your task is to design a set of stairs and a wheelchair ramp at the side. The cat starts at the bowl of milk. The cat travels 3 feet per second. Stage 1 Stage 2 Stage 3 All representations show a rate of change of -3 and an initial value of Jeff saves all of his money earned from delivering newspapers. Students will have many different ways of answering these questions. Look for and express regularity in repeated reasoning.

To make your examination easier choose two points that fall on an intersection of the gridlines.

# j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b – PDF

They also begin to understand how linear functions change. Graph and connect your new ordered pairs for the image on the coordinate plane in part a. Use the equation and graph to determine how many boys are on the team if Julie chose 18 girls. Examine the graphs and equations given above.

The graph below represents the girls trips to camp. Nate and Landon are competing in a 5 minute long Hot Dog eating contest. Write an equation that represents this relationship and use the equation to predict how tall the flower will be after 8 weeks. The table below represents how many balls she has as the season progresses; where x represents the number of weeks and y represents the number of tennis balls.

Your group task is to build a set of stairs and a handicap ramp at the side. Then complete the table, graph, and equation for your pattern.

In this section, students start by writing rules proportiojal linear patterns. Road Trip Context You are taking a road trip. Order the five activities from highest cost to lowest cost per hour. How deep should each step be? Fill in the missing items in the table if x represents the number of hours that have passed since Doug began pouring concrete and relatoinships represents the amount of concrete poured Time elapsed hours x Amount of concrete poured square feet y Graph the relationship below.

How would your context and equation change if the rate of change in this problem was changed to 2? Sufficient Mastery 3 I can find the unit rate for each relationship represented and then compare the unit rates to determine who makes more money.

## 2.3j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b

For example, if you dilate the set of points 0,00,43, 0and 3,4 with a scale factor of 2 and the center of dilation is at the origin 0,0 the distance of each point from the center will be 2 times as long prkportional it was originally. The sugar costs more to buy per pound.

What do you notice about the ratio y for Kelly? The statement below describes how unit rate defines y and x in a proportional proporional. Determine the rate of change and initial value of the function from a description of a relationship or from two x, y values, including reading these from a table or from a graph.

Help students to connect the 1 in the equation to the y-intercept on the graph. Proportional Relationships a Homework: Show where you see the rate of change in your table. The graph below represents what happened during the competition.

How many Dollars can you get for Euros?