to","points":1},{"id":"8ea8ad52-0295-4c6a-995c-da8b2e74a0a8","cardType":"basic","front":"What is the name of the constant $k$ in proportion equations?","back":"The constant of proportionality","points":1},{"id":"23be6d1d-e722-4a29-83d8-81e0c0906a94","cardType":"basic","front":"Write the formula for $A$ is directly proportional to the square of $B$.","back":"$$A = kB^2$","points":1},{"id":"c3769386-fc04-4868-8a92-f25a7baf2e5c","cardType":"basic","front":"Write the formula for $P$ is inversely proportional to the cube of $Q$.","back":"$$P = \\frac{k}{Q^3}$","points":1},{"id":"d5cfd15b-4998-4daf-8a4d-a16d633f384d","cardType":"cloze","front":"If $y$ is directly proportional to $x$, as $x$ increases, $y$ [ ] by the same scale factor.","back":"If $y$ is directly proportional to $x$, as $x$ increases, $y$ increases by the same scale factor.","points":null},{"id":"3f1ffbfd-2302-4546-8a28-853d1cfda2f6","cardType":"basic","front":"What are the three main steps to solve most proportion problems?","back":"

Write the formula with $k$
Substitute values to find $k$
Substitute the new value and solve

","points":3},{"id":"0090d7e8-608f-4c7a-9bed-7ec53db3f9ee","cardType":"basic","front":"In the inverse proportion formula $y = \\frac{k}{x}$, what calculation involving $x$ and $y$ always equals $k$?","back":"The product $xy$ (or $x \\times y$)","points":2},{"id":"3c5a4e89-652d-487d-927c-6531474d1b10","cardType":"cloze","front":"If $y$ is inversely proportional to $x$, as $x$ increases, $y$ [ ].","back":"If $y$ is inversely proportional to $x$, as $x$ increases, $y$ decreases.","points":null},{"id":"5cb23c98-66b0-4c0c-82f8-dd91b6afa9d5","cardType":"basic","front":"Identify the two required features of a direct proportion graph ($y \\propto x$).","back":"

Straight line
Passes through the origin (0,0)

","points":2},{"id":"6bcb51f3-8386-44f3-8f9b-7a608b3df93f","cardType":"basic","front":"Describe the graph of $y \\propto x^2$.","back":"A U-shaped curve (parabola) with its vertex at the origin.","points":2},{"id":"5f15582f-feea-4b56-b946-1e576fd76e66","cardType":"basic","front":"What does the graph of $y \\propto \\frac{1}{x}$ look like?","back":"Two curved branches (typically in the top-right and bottom-left quadrants).","points":2},{"id":"795b1f65-72b2-4f95-8123-adebb74ac3bc","cardType":"basic","front":"How does the graph of $y \\propto \\frac{1}{x^2}$ differ from $y \\propto \\frac{1}{x}$ regarding the x-axis?","back":"Both branches are above the x-axis (symmetric about the y-axis).","points":2},{"id":"beea19a0-900b-44df-8be2-47a62280129c","cardType":"cloze","front":"A straight line graph that [ ] does not represent direct proportion.","back":"A straight line graph that misses the origin does not represent direct proportion.","points":null},{"id":"7e1acbbc-1d4d-41b0-8892-480a0779b860","cardType":"basic","front":"Write the formula for $y$ being directly proportional to the square root of $x$.","back":"$$y = k\\sqrt{x}$","points":1},{"id":"dfbdbfe5-4fea-4dac-b269-a0dffb336da4","cardType":"basic","front":"How do you use a table of values to determine if $y \\propto x^2$ or $y \\propto x^3$?","back":"Test if $\\frac{y}{x^2}$ or $\\frac{y}{x^3}$ gives the same constant $k$ for every pair.","points":2},{"id":"cf8aa2fa-dd8b-4ced-b3af-879380bb429d","cardType":"cloze","front":"When solving $\\sqrt{s} = 3$, the value of $s$ is [ ].","back":

Direct and Inverse Proportion Flashcards

Direct and Inverse Proportion Flashcards

Direct and Inverse Proportion Flashcards

Direct and Inverse Proportion Flashcards