Write an equation that represents the relationship between the number of bags of popcorn that Agatha sells x and the amount of money she makes y. Prove that your pattern is linear using the representations geometric model, table, graph, and equation as evidence. A linear relationship is described by taking an initial value or starting point y-intercept and adding the rate of change times x. What do you notice about the ratio y for Grace? For each step you climb, you move up y inches and forward x inches. I can make and clearly label a graph that shows Jeff s savings.

No, there is not a constant ratio and the line does not go through the origin. Use the equation and graph to justify your answer. If students are using one of the methods mentioned they will run into difficulty finding the number of blocks in stage this gives purpose to finding an equation that relates the number of blocks to the stage number. Graph and write equations for a proportional relationship and identify the proportional constant or unit rate given a table, graph, equation, or context. The ratio is the same for Grace. Students will expand their understanding of discrete functions when they study sequences in Secondary I.

The graph shows a unit rate of WB This constant is called the constant of proportionality or proportional constant. Relatiknships Weeks of tennis balls a. Use the information given above to determine how much it will cost to relafionships 10 cupcakes at the bakery with the better deal.

The statement below describes how unit rate defines y and x in a proportional relationship. On your trip, you use 2 gallons per hour.

If they continue to struggle, ask them to draw stage 5 for you, explaining to you how they draw it. Sketch a graph for the four stories from number 1 relatuonships which you didn t choose in the space provided.

Fill in the boxes to show the relationship between white flowers and pink flowers in a vase. An airplane is at an elevation of ft. According to the graph it will take 6 miles to reach the ground.

Bryton states that each truck is traveling at a constant rate. This 2.1 shows the slope of your stairs. How long will it take Toby to cross the sidewalk? This will set the stage for students to be able to graph and write the equation of a line given any set of conditions. The unit rate for this relationship is two dollars for every bag of popcorn sold.

Create a table at the right which also pproportional the story of the graph and your homswork. If using a bottle, the water level in the bottle should be parallel to the side of the bottle. Compare the rate of change of both of the lines on the previous page by highlighting the change on the graph. The graph below shows the distance a cat is from his bowl of milk over time.

How did you draw your figure for stage 4 explain or show on the picture how you see the pattern growing from one stage to the next?

Write an equation that represents your proportional relationship. The rate of change is in both problems; however in Hillary s savings the initial value is pdoportional and in the landscaping problem, the initial value is Graph and connect the ordered pairs 0,00,43, 0and 3,4.

# Identify proportional relationships (practice) | Khan Academy

Write rules for linear patterns and connect the rule to the pattern geometric model. Trace the triangles by color.

Nate and Landon are competing in a 5 minute long Hot Dog eating contest. Make connections between the different representations. You may choose to explicitly discuss slope-intercept form earlier in the chapter if it materializes naturally in your classroom.

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

The smoothie was too tart because he did not add enough bananas to balance out the tartness of the strawberries. Point out how you can observe the proportional constant in each of them.

The pattern above is a linear pattern. Be sure prooortional label the columns in your table and the axes on your graph. I drew the corner square and realized that stage 4 would have four blocks on each arm attached to the corner block. How does the number of blocks in stage 0 relate to the simplified form of your rule? Most of the answers provided in this chapter give a continuous graph for the relationships. He gets paid the same rate every hour.