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rearrange the equation into the form $y = mx + c$.","code":"M"},{"id":"p2","marks":1,"description":"Correct gradient of 5.","code":"A"}],"finalAnswers":["5"],"generatedAt":"2026-05-07T01:55:12.602Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"rearrange_gradient_form","label":"Rearrange into gradient form","steps":[{"type":"text","order":0,"title":"Identify gradient form","content":"To read a gradient from a straight-line equation, first rearrange it into the form $y=mx+c$. Then the gradient can be identified from the coefficient of $x$.","highlights":[{"text":"Work out the gradient of this line.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@sky}{\\htmlData{anchor=original}{2y-10x=8}}$"},{"latex":"$$\\color{@orange}{\\htmlData{anchor=isolated}{2y=10x+8}}$"},{"latex":"$$\\color{@purple}{\\htmlData{anchor=divided}{y=\\frac{10}{2}x+\\frac{8}{2}}}$"},{"latex":"$$\\color{@green}{\\htmlData{anchor=simplified}{y=5x+4}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"original"},{"color":"orange","style":"text-color","anchor":"isolated"},{"color":"purple","style":"text-color","anchor":"divided"},{"color":"green","style":"text-color","anchor":"simplified"}],"connections":[{"to":"isolated","from":"original","color":"sky","label":"add 10x"},{"to":"divided","from":"isolated","color":"orange","label":"divide by 2"},{"to":"simplified","from":"divided","color":"purple","label":"simplify"}]},"order":1,"title":"Rearrange the equation","description":"First isolate the term containing y on the left, then divide every term by 2. Reaching the rearranged form earns the method mark."},{"type":"text","order":2,"title":"Read the gradient","content":"Now compare $y=5x+4$ with $y=mx+c$. The coefficient of $x$ is $5$, so the gradient is **$5$**. This earns the accuracy mark.","highlights":[{"text":"gradient of this line","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:53:02.713Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"556e202c-9d98-4591-816c-55ea03b37f00","label":"b","content":"Write down the equation of a line parallel to this line.","markscheme":"- Any line with $m = 5$, e.g., $y = 5x + 1$ B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Provides an equation with gradient 5.","code":"B"}],"finalAnswers":["y=5x+1"],"generatedAt":"2026-05-07T01:55:12.602Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":64},"walkthroughVideo":null},{"id":"d1df5b75-7197-44b8-9ce1-7e278727d4dc","revisionId":"d5dec3ee-328b-4d02-9c53-c4a541a6d8cf","questionNumber":"10","questionType":"LA","specification":"A straight line has equation $4y - 5x = 2$","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Equation of a Line","calculatorUse":null,"isCalculation":true,"parts":[{"id":"7594ea61-c78f-443d-a5e9-09ef9d400d6e","label":"a","content":"Work out the gradient of this line.","markscheme":"- Rearranges to $4y = 5x + 2$ or $y = \\frac{5}{4}x + \\frac{1}{2}$ M1\n- Gradient is $\\frac{5}{4}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Attempts to rearrange the equation into the form $y = mx + c$.","code":"M"},{"id":"p2","marks":1,"description":"Correct gradient of $\\frac{5}{4}$ or 1.25.","code":"A"}],"finalAnswers":["5/4","1.25"],"generatedAt":"2026-05-07T01:55:12.602Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"rearrange_gradient_form","label":"Rearrange into gradient form","steps":[{"type":"text","order":0,"title":"Recall gradient form","content":"A straight line written as $y=mx+c$ has gradient $m$, the coefficient of $x$. So rearrange the given equation until $y$ is on its own.","highlights":[{"text":"Work out the gradient of this line.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4y-\\color{@sky}{\\htmlData{anchor=negative_x}{5x}}=2$"},{"latex":"$$4y=\\color{@sky}{\\htmlData{anchor=positive_x}{5x}}+2$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"negative_x"},{"color":"sky","style":"text-color","anchor":"positive_x"}]},"order":1,"title":"Move the x-term","description":"Add 5x to both sides. Reaching this rearrangement earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4y=5x+2$"},{"latex":"$$\\dfrac{4y}{\\color{@orange}{\\htmlData{anchor=divisor_left}{4}}}=\\dfrac{5x}{\\color{@orange}{\\htmlData{anchor=divisor_x}{4}}}+\\dfrac{2}{\\color{@orange}{\\htmlData{anchor=divisor_constant}{4}}}$"},{"latex":"$$y=\\dfrac{5}{4}x+\\dfrac{1}{2}$"}],"highlights":[{"color":"orange","style":"text-color-with-background","anchor":"divisor_left"},{"color":"orange","style":"text-color-with-background","anchor":"divisor_x"},{"color":"orange","style":"text-color-with-background","anchor":"divisor_constant"}]},"order":2,"title":"Divide by four","description":"Divide every term by 4 so that y is on its own."},{"type":"text","order":3,"title":"Read the gradient","content":"Comparing $y=\\frac{5}{4}x+\\frac{1}{2}$ with $y=mx+c$, the coefficient of $x$ is $\\frac{5}{4}$. Therefore, the gradient is\n\n$$\\boxed{\\frac{5}{4}}$$\n\nThis correct value earns A1.","highlights":[{"text":"gradient","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:45:06.530Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"60431b0c-e4d3-487a-ab4d-41d3eb2d56a8","label":"b","content":"Write down the equation of a line parallel to this line.","markscheme":"- Any line with $m = \\frac{5}{4}$, e.g., $y = \\frac{5}{4}x + 1$ B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Provides an equation with gradient $\\frac{5}{4}$.","code":"B"}],"finalAnswers":["y=5/4x+1"],"generatedAt":"2026-05-07T01:55:12.602Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"match_the_gradient","label":"Match the gradient","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4y-5x=2$"},{"latex":"$$4y=5x+2\\;\\htmlData{anchor=divideStart}{\\kern1.5em}$"},{"latex":"$$y=\\frac{5}{4}x+\\frac{1}{2}\\;\\htmlData{anchor=divideEnd}{\\kern1.5em}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"divideStart"},{"color":"sky","style":"text-color","anchor":"divideEnd"}],"connections":[{"to":"divideEnd","from":"divideStart","color":"sky","label":"divide every term by 4","style":"solid"}]},"order":0,"title":"Find the gradient","description":"Rearrange into the form y = mx + c, where m is the gradient. Dividing every term by 4 gives the gradient needed for a parallel line."},{"type":"text","order":1,"title":"Keep the gradient","content":"Parallel lines have the same gradient, so the new line must also have gradient $\\frac54$. Choose a different intercept so it is a different parallel line.","highlights":[{"text":"parallel to this line","location":"specification"}]},{"type":"text","order":2,"title":"Write one equation","content":"For example,\n\n$$\\boxed{y=\\frac54x+1}$$\n\nIts gradient is $\\frac54$, so it is parallel to the given line. This earns **B1**. Many answers are possible: any equation with gradient $\\frac54$ and an intercept different from $\\frac12$ is valid."}]}],"generatedAt":"2026-07-20T16:51:14.139Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":75},"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"5d14ecc1-58c6-473c-9cb7-fca27206b294","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"649f2074-9021-4166-b009-d220b59e51b3","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"87a8c625-0bee-4286-afe3-0a37149b2c7b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"bd5dab9e-24b4-4087-89c6-ab83d6180d24","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"aa2033de-d33c-40cf-9234-e060de817401","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d14cff85-5d3b-47e2-b198-1bc33014e080","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"17292aa6-1769-4e32-bc6e-a6a3ae79bd4c","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d1df5b75-7197-44b8-9ce1-7e278727d4dc","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Equation of a Line","topicId":"5e752746-ffc9-406f-9ef5-d37bf7d64843","topicSidebar":"$L3b","topicSlug":"grade-6-6-8-equation-of-a-line","topicTitle":"Equation of a Line"}]}],"$L3c","$L3d"]}]

Equation of a Line

Question 2

Equation of a Line Questions

Equation of a Line

Question 2

Equation of a Line Questions