{"id":218,"date":"2022-04-12T09:55:17","date_gmt":"2022-04-12T09:55:17","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=218"},"modified":"2025-12-19T05:36:21","modified_gmt":"2025-12-19T05:36:21","slug":"j-14-constant-rate-of-change","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/j-14-constant-rate-of-change\/","title":{"rendered":"J.14 Constant rate of change"},"content":{"rendered":"\n

Constant rate of change<\/strong><\/h2>\n\n\n\n

Key notes:<\/p>\n\n\n\n

\ud83d\udd39 What is Constant Rate of Change?<\/strong><\/p>\n\n\n\n

It means a quantity changes by the same amount every time<\/strong> \ud83d\udcca.
\ud83d\udc49 The change is steady and predictable<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 Simple Meaning \ud83e\udde0<\/strong><\/p>\n\n\n\n

If one value goes up (or down), the other value changes equally each time<\/strong> \u2795\u2796.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 Real-Life Examples \ud83c\udf0d<\/strong><\/p>\n\n\n\n

\ud83d\udeb6 Walking at the same speed
\ud83d\udcb0 Saving \u20b9100 every week
\ud83d\ude97 A car moving 60 km every hour<\/p>\n\n\n\n

All these show a constant rate of change<\/strong> \u2714\ufe0f<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 In Tables \ud83d\udccb<\/strong><\/p>\n\n\n\n

If the difference between numbers is always the same<\/strong>, the rate is constant.
Example:
2, 4, 6, 8 \u2192 increases by +2 each time<\/strong> \u2795\u2795<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 In Graphs \ud83d\udcc9<\/strong><\/p>\n\n\n\n

\ud83d\udccd A straight line<\/strong> shows a constant rate of change
\ud83d\udccd The line can go upward<\/strong> \u2b06\ufe0f or downward<\/strong> \u2b07\ufe0f<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 Positive vs Negative Rate \ud83d\udd04<\/strong><\/p>\n\n\n\n

\u2795 Positive rate<\/strong>: values increase (line goes up \ud83d\udcc8)
\u2796 Negative rate<\/strong>: values decrease (line goes down \ud83d\udcc9)<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 Slope Connection \ud83d\udcd0<\/strong><\/p>\n\n\n\n

The constant rate of change is also called the slope<\/strong> of a line.
\ud83e\uddee Slope = change in y \u00f7 change in x<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd39 Key Words to Remember \ud83d\udcdd<\/strong><\/p>\n\n\n\n

\u2705 Constant
\u2705 Same change
\u2705 Straight line
\u2705 Slope
\u2705 Steady speed<\/p>\n\n\n\n

\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

\ud83d\udccd This graph shows how the amount of time that a receptionist named Colette spends on the phone is related to the number of phone calls she routes to employees.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the rate of change?<\/strong><\/p>\n\n\n\n

Write your answer as a decimal or integer.<\/em><\/p>\n\n\n\n

 ______ minutes per phone call<\/p>\n<\/div><\/div>\n\n\n\n

Find any two points on the line.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Two points on the line are (0, 30) and (40, 60). Put those points into the slope formula.<\/p>\n\n\n\n

slope = change in y \/ change in x<\/p>\n\n\n\n

= 60 – 30 \/ 40 – 0 Plug in (0, 30) and (40, 60)<\/p>\n\n\n\n

= 30 \/ 40 Subtract<\/p>\n\n\n\n

= 3\/4 Subtract<\/p>\n\n\n\n

= 0.75 Write as a decimal<\/p>\n\n\n\n

The slope is 0.75. The rate of change is 0.75 minutes per phone call.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\ud83d\udccd This graph shows how the number of cakes Donald can bake is related to the number of additional sticks of butter he buys.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the rate of change?<\/strong><\/p>\n\n\n\n

Write your answer as a decimal or integer.<\/p>\n\n\n\n

_______ cakes per stick of butter<\/p>\n<\/div><\/div>\n\n\n\n

Find any two points on the line.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Two points on the line are (0, 3) and (1, 5). Put those points into the slope formula.<\/p>\n\n\n\n

slope = change in y \/ change in x<\/p>\n\n\n\n

= 5 – 3 \/ 1 – 0 Plug in (0, 3) and (1, 5)<\/p>\n\n\n\n

= 2\/1 Subtract<\/em><\/p>\n\n\n\n

= 2 Subtract<\/em><\/p>\n\n\n\n

The slope is 2. The rate of change is 2 cakes per stick of butter.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\ud83d\udccd This graph shows how the amount of time that a receptionist named Danny spends on the phone is related to the number of phone calls he routes to employees.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the rate of change?<\/strong><\/p>\n\n\n\n

Write your answer as a decimal or integer.<\/em><\/p>\n\n\n\n

 _________ minutes per phone call<\/p>\n<\/div><\/div>\n\n\n\n

Find any two points on the line.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Two points on the line are (0, 3) and (5, 4). Put those points into the slope formula.<\/p>\n\n\n\n

slope = change in y \/ change in x<\/p>\n\n\n\n

= 4 – 3 \/ 5 – 0 Plug in (0, 3) and (5, 4)<\/p>\n\n\n\n

= 1\/5 Subtract <\/p>\n\n\n\n

= 0 . 2 Write as a decimal<\/p>\n\n\n\n

The slope is 0.2. The rate of change is 0.20 minutes per phone call.<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice! \ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\n\n\n\n

\n
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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Constant rate of change Key notes: \ud83d\udd39 What is Constant Rate of Change? It means a quantity changes by the same amount every time \ud83d\udcca.\ud83d\udc49 The change is steady and predictable. \ud83d\udd39 Simple Meaning \ud83e\udde0 If one value goes up (or down), the other value changes equally each time \u2795\u2796. \ud83d\udd39 Real-Life Examples \ud83c\udf0d \ud83d\udeb6Continue reading “J.14 Constant rate of change”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-218","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=218"}],"version-history":[{"count":11,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/218\/revisions"}],"predecessor-version":[{"id":17668,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/218\/revisions\/17668"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}