# Compare Linear Relationships Given Different Forms Quiz

7 questions

### #1 of 7:Mild

Compare linear relationships given different forms

<p>Ms.Ortega is teaching two different after-school robotics classes. She has some supplies on hand, and calculates the cost per robot after purchasing supplies. </p><p>For Robot type A she uses the equation `y = 18x+45` to determine the total cost of the materials `(y)` where `x` represents the number of robots.</p><p>For Robot type B, she creates a table to show the total cost of the materials.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Robots `(x)`" }, { "value": "Total cost `(y` dollars`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`40`" } ], [ { "value": "`1`" }, { "value": "`56`" } ], [ { "value": "`2`" }, { "value": "`72`" } ] ]}'></TableUIv2 ><ul><li>Which robot has a lower cost per robot? </li><li>What is the difference in cost per robot?</li><li>Which robot had a lower amount for supplies on hand? What is the difference in the value of supplies on hand?</li></ul>

### #2 of 7:Mild

Compare linear relationships given different forms

<p>Shaun is comparing rates at two dog daycares. </p><p>Lucky Dog Daycare uses the equation `y = 10x + 25` to determine the total cost `(y)`, where `x` represents the number of visits.</p><p>Woof Daycare shows Shaun a graph that represents their prices.</p><LineGraph data-props='{ "options": { "x_min": 0, "y_min": 0, "y_max": 100, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 10, "x_label": "Number of Visits", "y_label": "Cost (dollars)", "title": " ", "x_axis_name": " ", "y_axis_name": " " }, "points": [ { "id": 0, "x": 0, "y": 30, "show_point": false, "highlight_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false }, { "id": 1, "x": 4, "y": 50, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false }, { "id": 2, "x": 8, "y": 70, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false }, { "id": 3, "x": 10, "y": 80, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": true, "highlight_line": "#000000" } ]}'></LineGraph ><ul><li>Which daycare charges less for each visit? </li><li>What is the difference in the cost per visit?</li><li>Which daycare has a lower initial fee?</li><li> What is the difference in initial fees?</li></ul>

### #3 of 7:Medium

Compare linear relationships given different forms

<p>A party shop sells two piñatas filled with candy. </p><p>The equation `y = 3.5x + 25` represents the total cost of the dinosaur piñata `(y)` where `x` is the cost per pound of the candy.</p><p>The cost total cost of the unicorn piñata is shown in the graph.</p><LineGraph data-props='{ "options": { "x_min": 0, "y_min": 16, "y_max": 34, "x_max": 9, "cell_size": 20, "x_interval": 1, "y_interval": 2, "x_label": "Amount of Candy (pounds)", "y_label": "Total Cost (dollars)", "title": " ", "x_axis_name": " ", "y_axis_name": " " }, "points": [ { "id": 0, "x": 0, "y": 22, "show_point": false, "highlight_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false }, { "id": 1, "x": 4, "y": 34, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": true, "highlight_line": "#000000" } ]}'></LineGraph ><ul><li>Which piñata is filled with less expensive candy?</li><li> What is the difference in the price per pound for the candy?</li><li>Which piñata is less expensive unfilled? </li><li>What is the difference in the unfilled costs of the piñatas?</li></ul>

### #4 of 7:Medium

Compare linear relationships given different forms

<p>Patrick is deciding what kind of tree to plant in his backyard.</p><p>He uses the equation `y = 2x +8` to represent the total height `(y)` of an oak tree, where `x` represents the expected growth each year.</p><p>The table represents the expected growth for a dogwood tree.</p><TableUIv2 data-props='{ "headers": [ { "value": "Amount of Time `(x` years`)`" }, { "value": "Total Height `(y` ft`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`6`" } ], [ { "value": "`3`" }, { "value": "`15`" } ], [ { "value": "`6`" }, { "value": "`24`" } ] ]}'></TableUIv2 ><ul><li>Which tree is expected to grow more per year? </li><li>What is the difference in the exptected growth for each tree per year?</li><li>Which tree is taller to start with? </li><li>What is the difference in starting height for the two trees?</li></ul>

### #5 of 7:Medium

Compare linear relationships given different forms

<p>Annabelle and Hank both collect baseball cards.</p><p>Annabelle use the equation `y = 10x +100` to determine the number of cards in her collection `(y)`, where `x` represents the number she adds each month.</p><p>Hank uses a table to represent the number of cards in his collection.</p><TableUIv2 data-props='{ "headers": [ { "value": "Amount of Time `(x` months`)`" }, { "value": "Total Cards `(y)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`65`" } ], [ { "value": "`3`" }, { "value": "`110`" } ], [ { "value": "`6`" }, { "value": "`155`" } ] ]}'></TableUIv2 ><ul><li>Which person gets more cards per month? </li><li>What is the difference in the number of cards per month for both collectors?</li><li>Which collection has more cards to start with? </li><li>What is the difference in the number of starting cards in the collection?</li></ul>

### #6 of 7:Spicy

Compare linear relationships given different forms

<p>Roman and Sawyer are each building birdhouses to sell at an artist's market. They want to compare their overall costs.</p><p>Roman uses the equation `y = 7.5x + 38` to determine his total costs `(y`), where `x` represents the number of bird houses.</p><p>Sawyer uses the table to represent her total costs.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Birdhouses `(x)`" }, { "value": "Total Cost `(y` dollars`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`40`" } ], [ { "value": "`3`" }, { "value": "`60.25`" } ], [ { "value": "`6`" }, { "value": "`80.50`" } ] ]}'></TableUIv2 ><ul><li>Which person has higher costs per birdhouse? </li><li>What is the difference in the cost per birdhouse?</li><li>Which person spent more on construction tools?</li><li> What is the difference in the cost of the tools for each builder?</li></ul>

### #7 of 7:Spicy

Compare linear relationships given different forms

<p>Vin and Nancy are both sewing costumes for the school play.</p><p>Vin uses the equation `y = 9.5x+30` to determine the total cost of the project `(y)` where `x` represents the number of yards of fabric.</p><p>Nancy shows her costs in the table.</p><TableUIv2 data-props='{ "headers": [ { "value": "Amount of Fabric `(x` yards`)`" }, { "value": "Total Cost `(y` dollars`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`25`" } ], [ { "value": "`2`" }, { "value": "`40`" } ], [ { "value": "`4`" }, { "value": "`55`" } ] ]}'></TableUIv2 ><ul><li>Which person has a lower cost for each yard of fabric? </li><li>What is the difference in cost per yard?</li><li>Which person has a lower cost for initial supplies?</li><li> What is the difference in cost for initial supplies?</li></ul>

In 8th Grade, students learn how to compare linear relationships. Teachers can use  "Compare linear relationships given different forms" to test the ability of the students to analyze and compare the linear relationships represented by equations, graphs, or tables.

In this quiz, two relationships are given in the form of equations, graphs, or tables, and students are asked some questions which compare both relationships. Using this quiz, teachers can easily identify the knowledge gaps of the students and help them to understand this concept better.

In 8th Grade, students learn how to compare linear relationships. Teachers can use  "Compare linear relationships given different forms" to test the ability of the students to analyze and compare the linear relationships represented by equations, graphs, or tables.

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Linear Relationships And Functions
8.F.A.2

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### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”