{"id":"study-phone-plan-slope-meaning","audience":"high-school","category":"explaining","technique":"examples","track":"study","title":"Understand slope and intercept in a phone plan problem","free":false,"task":"Your Algebra 1 homework asks what the slope and y-intercept mean in a phone plan problem. Get exactly 3 numbered lines that start with the part letters (a), (b) and (c): the slope and what it means, the y-intercept and what it means, and the 6 GB bill with the math shown, plain text, under 75 words. Use the corrected plan price from Mr. Novak's note.","materialLabel":"The homework problem and teacher note (attached to your prompt automatically)","material":"ALGEBRA 1 - Mr. Novak - HW 5.3: Slope in context - #4\n\nBluewave Mobile's plan: monthly cost C = 8g + 20, where g = gigabytes (GB) of data used.\n\n(a) What is the slope, and what does it mean in this situation?\n(b) What is the y-intercept, and what does it mean?\n(c) How much would the bill be if you used 6 GB?\n\n** Mr. Novak's note (Google Classroom): \"Typo in #4: the base fee is $15, not $20. The equation should be C = 8g + 15.\" **\n\nFrom class:\n- Slope = rate of change (\"per\" something). Units matter: dollars per GB.\n- y-intercept = the value when x (here g) is 0. \"What you pay even if you use nothing.\"\n\nMy confusion: I can find the numbers but don't know how to say what they MEAN.\nHW due Thursday.","rules":[{"type":"numberedItems","count":3},{"type":"maxWords","max":75},{"type":"plainText"}],"mistakes":[{"title":"Asking what slope is","why":"The AI defines slope in general and never ties it to the phone plan.","fix":"Ask for meaning: \"Say what the slope and intercept mean for this plan.\"","checks":["r0","r1"]},{"title":"Missing the correction","why":"The typo and the fix are both in your material.","fix":"Add: \"Use C = 8g + 15 from Mr. Novak's note.\"","checks":["r1","r2"]},{"title":"Not saying how many lines","why":"The AI picks its own number, and it usually picks more lines than you need.","fix":"Be exact: \"Exactly 3 numbered lines.\"","checks":["numberedItems"]},{"title":"Not showing the math","why":"A bare total doesn't show you how to set it up.","fix":"Add: \"Show 8(6) + 15 for the 6 GB bill.\"","checks":["r2"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each line: \"each under 20 words.\"","checks":["maxWords"]},{"title":"Forgetting where it will be read","why":"AI formats for a screen, with bold and headings that show up as stray symbols in your homework.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Uses the part letters","patterns":["\\(a\\)","part letter","\\(b\\)"]},{"label":"Uses the correction","patterns":["15","correct","typo"]},{"label":"Says how many lines","patterns":["\\b(3|three)\\b.{0,25}line"]},{"label":"Asks to show the math","patterns":["show.{0,15}(math|work)","8 ?\\(6\\)","8 ?x ?6"]},{"label":"Sets a length limit","patterns":["\\d+\\s*words","word (limit|count)","under \\d+"]}],"hint":"The hard part is saying what the numbers mean. Ask for each one with its meaning in the plan, the math for the bill, and the corrected equation.","rubricLabels":["Line 1 starts with '(a)' and gives the slope as 8, meaning $8 per GB of data","Line 2 starts with '(b)' and gives the y-intercept as 15 (the correction, not 20), meaning the $15 base fee you pay even with 0 GB","Line 3 starts with '(c)' and shows the math for 6 GB with the corrected equation: 8(6) + 15 = $63 (not $68)"]}