They will use proportionality produced by a dilation to do this derivation. How do you compare the cost per hour by looking at the graph? When we do that, we get! Find and describe the unit rate for Besty s smoothie. I don t know how to write a rule for the pattern.
Create a table at the right which also tells the story of the graph and your writing. Label each line with the candy it represents. What do you observe about the transformation when you do it graphically and algebraically? She does not take out or put in any money into her account for 5 weeks. Point out how you can observe the proportional constant in each of them. Don did not add the right amount of bananas he doubled the amount of strawberries by adding 2 cups, but he also added 2 bananas.
Euros x Dollars y WB Students use their knowledge of slope and proportionality to represent and construct hhe functions in a variety of ways. Know that the graph of a proportional relationship goes through the origin.
Separate your answers homework a comma. Green lines are possible answers. When we do that, we get! Right triangles that are formed from any two distinct points on a line are dilations of one another. Proportional Relationships b Class Activity: Reversing Diabetes Summit There Reviews: Find the exchange rate for Dollars y to Euros x. Graph the relationship on the grid below.
j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b – PDF
Sue drives miles and uses Use equations and connects to compare fuel efficiency and to determine the costs of various trips. Agatha s relationship shows a special homdwork where the linear relationship is also proportional. Graph this relationship on the same coordinate plane as Tuesday s information on the previous page. Find the unit rate for each boy s truck. Express the proportional constant as a unit rate. Think about all of the equations that you have written to represent a linear relationship, what do they have in common, what do the different parts of the equations represent?
Ask them to compare the proportional constant or unit rate for their relationship with the other members of their group.
Summarize what you know about proportional relationships using bulleted list in the space below. It is an asset to ths information such as membership in professional associations.
Find patetrn unit rate for this proportional relationship. From the two points create a right triangle, the line itself will be the hypotenuse and homewor, legs will extend from the two points and meet at a right angle. This constant rate of change makes the line straight. Point out that in this case the number of ounces of extract is defined as x and the pounds of dry ice is defined as y.
Students move fluently between the representations of a linear relationship and make connections between the representations. Find the slope of the waterslide. Consider the relationship between the number of years from now and the number of students enrolled.
To confirm this, investigate this transformation below. Agatha s relationship is proportional because a proportional constant of 2 relates the number 1 of bags of popcorn she sells to the amount of money she makes. Graph and write equations for a proportional relationship and identify the proportional constant or unit rate given a table, graph, equation, or context. 2.2s graph below shows the distance a mouse is from her cheese over time.
If Carmen uses 12 pounds of dry ice she will need to use 8 ounces of root connevt extract. If the information is given in a table, fill in the story and equation.
2.2a homework connect the rule to the pattern
Toby travels at a rate of. Use the ordered pairs given in the table to test your chosen equation and explain your choice. This conceptual foundation will set the stage for students to be able to derive the equation of a line using dilations in section 2.
The pattern is linear.