Compare Linear Relationships Given Different Forms Quiz

<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>

<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>

<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>

<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>

<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>

<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>

<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>