Compare Linear Relationships Given Different Forms

<p>Mavis and Emily each start reading books during a weekend at the beach.</p><p>Mavis uses the equation `y = 45x + 38` to see how many pages she will have read `(y)` where `x` represents the number of days of reading.</p><p>Emily used a table to track her progress.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Days `(x)`" }, { "value": "Total pages `(y)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`32`" } ], [ { "value": "`1`" }, { "value": "`62`" } ], [ { "value": "`2`" }, { "value": "`92`" } ] ]}'></TableUIv2 ><ul><li>Which person reads more pages per day?</li><li> What is the difference in the number of pages read per day?</li><li>Which person read more pages while at the beach? </li><li>What is the difference in the number of pages they each read at the beach?</li></ul>

<p>Devin and Elle are both contributing to their savings accounts while working summer jobs. </p><p>Devin uses the equation `y = 185 + 25x` to determine the balance of his account `(y)` where `x` represents the number of weeks he adds to the account.</p><p>Elle uses a graph to represent the balance in her account.</p><LineGraph data-props='{ "options": { "x_min": 0, "y_min": 200, "y_max":410, "x_max": 9, "cell_size": 20, "x_interval": 1, "y_interval": 30, "x_label": "Number of Weeks", "y_label": "Saving Accounts Balance (dollars)", "title": " ", "x_axis_name": " ", "y_axis_name": " " }, "points": [ { "id": 0, "x": 0, "y": 200, "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": 6, "y": 320, "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": 2, "x": 9, "y": 380, "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": 2, "show_start_arrow": false, "show_end_arrow": true, "highlight_line": "#000000" } ]}'></LineGraph ><ul><li>Which person contributes more to their account per week? </li><li>What is the difference in the amount of the weekly contribution?</li><li>Which person had more in their account before they started the weekly deposits?</li><li> What is the difference in the beginning balance?</li></ul>

<p>Big Juice is comparing its smoothie prices to Tasty Juice.</p><p>Big Juice uses the equation `y = 0.25x + 4` to determine the cost `(y)` of a banana smoothie were `x` represents the number of added ingredients.</p><p>Tasty Juice uses a graph to represent their price for a banana smoothie.</p> <LineGraph data-props='{ "options": { "x_min": 0, "y_min": 0, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1, "x_label": "Number of Added Ingredients", "y_label": "Cost (dollars)", "title": " ", "x_axis_name": " ", "y_axis_name": " " }, "points": [ { "id": 0, "x": 0, "y": 3, "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": 8, "y": 7, "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": 10, "y": 8, "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": 2, "show_start_arrow": false, "show_end_arrow": true, "highlight_line": "#000000" } ]}'></LineGraph ><ul><li>Which company charges less for each added ingredient?</li><li>What is the difference in the cost per ingredient?</li> <li>Which company has a lower cost for the banana smoothie with no added ingredients? </li><li>What is the difference in the cost?</li></ul>

<p>Jasper is comparing the cost for a large pizza at two restaurants.</p><p>Saucy uses the equation `y = 2.5x + 18` to determine the cost of the pizza `(y)`, where `x` represents the number of toppings.</p><p>Pie Five represents their cost with a table.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Toppings `(x)`" }, { "value": "Total Cost `(y ` dollars`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`17`" } ], [ { "value": "`2`" }, { "value": "`23`" } ], [ { "value": "`4`" }, { "value": "`29`" } ] ]}'></TableUIv2 ><ul><li>Which company charges less for each pizza topping? </li><li>What is the difference in the cost per topping?</li><li>Which restaurant charges less for the plain pizza? </li><li>What is the difference in costs for the plain pizza?</li></ul>

<p> Amber and Yuri each spend time over the weekend working on upcoming projects for school. They want to compare their total homework time for the week.</p><p>Amber uses the equation `y = 1.5x + 2.5` to determine the total amount of homework time for the week `(y)`, where `x` represents the number of nights she spent doing homework.</p><p>Yuri's homework time is represented by the table.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Nights `(x)`" }, { "value": "Amount of Homework `(y` hours`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`3.75`" } ], [ { "value": "`2`" }, { "value": "`6.25`" } ], [ { "value": "`4`" }, { "value": "`8.75`" } ] ]}'></TableUIv2 ><ul><li>Which person spends less time per night doing homework? </li><li>What is the difference in the amount of nightly homework?</li><li>Which person did more homework over the weekend? </li><li>What is the difference in the amount of homework over the weekend? </li></ul>

<p>Isaac and Hannah play in different school bands. They each had a concert this month and they want to compare the time they spend playing.</p><p>Isaac uses the equation `y = 0.75x + 1.5` to represent the amount of time he spent playing his tuba `(y)`, where `x` represents the number of days he has practiced.</p><p>Hannah uses the table to represent the amount of time she spent playing her trombone.</p><TableUIv2 data-props='{ "headers": [ { "value": "Number of Days `(x)`" }, { "value": "Amount of Time `(y` hours`)`" } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`1.75`" } ], [ { "value": "`2`" }, { "value": "`4.25`" } ], [ { "value": "`4`" }, { "value": "`6.75`" } ] ]}'></TableUIv2 ><ul><li>Which person practices more per day? </li><li>What is the difference in the amount of practice time per day?</li><li>Which student spent more time at their concert? </li><li>What is the difference in the amount of time spent at the concert?</li></ul>

<p>Judy keeps two kiddie pools in her backyard for her dogs to play in. She tops them both off one hot afternoon using two different hoses.</p><p>For the smaller pool, she uses the equation `y = 8.5x +20` to determine the total number of gallons `(y)` in the pool, where `x` represents the number of minutes the hose has been running.</p><p>The table represents the number of gallons in the larger pool.</p><TableUIv2 data-props='{ "headers": [ { "value": "Time `(x` minutes`)`" }, { "value": "Total Water `(y` gallons`)` " } ], "borders": { "rows": [], "cols": [] }, "rows": [ [ { "value": "`0`" }, { "value": "`25`" } ], [ { "value": "`2`" }, { "value": "`44`" } ], [ { "value": "`4`" }, { "value": "`63`" } ] ]}'></TableUIv2 ><ul><li>Which pool is being filled with more water per minute?</li><li> What is the difference in the amount of water per minute?</li><li>Which pool had more water to start with? </li><li>What is the difference in the amount of starting water in each pool?</li></ul>