Compare Linear Relationships Given Different Forms

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#1 of 7: Mild

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>

#2 of 7: Medium

Compare linear relationships given different forms

<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>

#3 of 7: Medium

Compare linear relationships given different forms

<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>

#4 of 7: Medium

Compare linear relationships given different forms

<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>

#5 of 7: Spicy

Compare linear relationships given different forms

<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>

#6 of 7: Spicy

Compare linear relationships given different forms

<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>

#7 of 7: Spicy

Compare linear relationships given different forms

<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>

For 8th Grade, a linear relationship is an essential topic and it also plays a crucial role in higher-level mathematics. In order to become proficient in understanding linear relationships, the student can use “Compare linear relationships given different forms practice problems”. 

 

In these problems, students need to compare linear relationships given in different forms such as equations, graphs, or tables. It can help students identify key components of the linear relationships such as slope and y-intercept and interpret real-world scenarios.

For 8th Grade, a linear relationship is an essential topic and it also plays a crucial role in higher-level mathematics. In order to become proficient in understanding linear relationships, the student can use “Compare linear relationships given different forms practice problems”. 

 

In these problems, students need to compare linear relationships given in different forms such as equations, graphs, or tables. It can help students identify key components of the linear relationships such as slope and y-intercept and interpret real-world scenarios.

For 8th Grade, a linear relationship is an essential topic and it also plays a crucial role in higher-level mathematics. In order to become proficient in understanding linear relationships, the student can use “Compare linear relationships given different forms practice problems”. ...

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Grade 8
Linear Relationships And Functions
8.F.A.2

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What teachers are saying about BytelearnWhat teachers are saying

stephan.png
Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
jennifer.png
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.png
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”