Transcript: gradient,_intercepts_&_straight-line_graphs_in_the_20250910_065656.html

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[
  {
    "slide": 1,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Lines, Slopes & Cuts\nDiscover the story every straight line tells.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 2,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "The Coordinate Grid",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Coordinate Plane\nTwo perpendicular number lines—the horizontal x-axis and vertical y-axis—meet at the origin \\( (0,0) \\). Locations are written as ordered pairs \\( (x,y) \\).",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Key Characteristics:\nHorizontal x-axis shows left–right values.\nVertical y-axis shows up–down values.\nAxes intersect at the origin \\( (0,0) \\).\nEach point is written as \\( (x,y) \\).",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Example:\nPlot \\( (-2,3) \\) — it sits in Quadrant II.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 3,
    "fragments": [
      {
        "fragment_index": 1,
        "text_description": "What Is Gradient?",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Term\nGradient (Slope)\nDefinition\nMeasure of a line’s steepness — how far it rises or falls for each unit you move right.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Rise ÷ Run\nPositive: Upward tilt\nNegative: Downward tilt",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Example: Gradient 2 means the line rises 2 units for every 1 unit across.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 4,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Seeing Gradient",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Arrows show 6-unit rise and 4-unit run.",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/aUvPedzYsMfpPhH2tG55e5zsZjbcKu5T9Ns8y6vG.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Gradient = Rise ÷ Run\nVertical rise = 6 units; horizontal run = 4 units.\nTherefore \\( \\text{gradient} = \\frac{6}{4} = 1.5 \\).\nKey Points:\nrise = change in \\(y\\)\nrun = change in \\(x\\)\ngradient shows line steepness",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 5,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Gradient Formula\nApplications",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "\\[m = \\frac{y_2 - y_1}{x_2 - x_1}\\]\nThe slope formula uses any two distinct points on a non-vertical straight line; the ratio is constant.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Variable Definitions\n\\(m\\)\ngradient (slope)\n\\(x_1\\)\nx-coordinate of first point\n\\(y_1\\)\ny-coordinate of first point\n\\(x_2\\)\nx-coordinate of second point\n\\(y_2\\)\ny-coordinate of second point",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Find slope\nCalculate how steep a line is between two given points.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Write line equation\nUse \\(m\\) with one point to form \\(y = mx + c\\).",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 6,
    "fragments": [
      {
        "fragment_index": 1,
        "text_description": "Match Rise & Run",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Active practice: drag each run number to the corresponding rise so the gradient \\(m=\\frac{\\text{rise}}{\\text{run}}\\) is correct.",
        "image_description": ""
      },
      {
        "fragment_index": -1,
        "text_description": "Draggable Items\nDrop Zones\nTip:\nRemember: \\(m=\\frac{\\text{rise}}{\\text{run}}\\). Swap rise or run to get the needed ratio.\nCheck Answers\nResults\n// Drag and drop functionality\n        const draggableItems = document.querySelectorAll('.draggable-item');\n        const dropZones = document.querySelectorAll('.drop-zone');\n        const checkAnswersBtn = document.getElementById('checkAnswersBtn');\n        const feedbackArea = document.getElementById('feedbackArea');\n        const feedbackContent = document.getElementById('feedbackContent');\n        \n        // Drag and drop event listeners\n        draggableItems.forEach(item => {\n            item.addEventListener('dragstart', handleDragStart);\n            item.addEventListener('dragend', handleDragEnd);\n        });\n        \n        dropZones.forEach(zone => {\n            zone.addEventListener('dragover', handleDragOver);\n            zone.addEventListener('drop', handleDrop);\n            zone.addEventListener('dragenter', handleDragEnter);\n            zone.addEventListener('dragleave', handleDragLeave);\n        });\n        \n        function handleDragStart(e) {\n            e.target.classList.add('opacity-50');\n            e.dataTransfer.setData('text/plain', e.target.dataset.id);\n        }\n        \n        function handleDragEnd(e) {\n            e.target.classList.remove('opacity-50');\n        }\n        \n        function handleDragOver(e) {\n            e.preventDefault();\n        }\n        \n        function handleDragEnter(e) {\n            e.preventDefault();\n            e.target.closest('.drop-zone').classList.add('border-green-500', 'bg-green-50');\n        }\n        \n        function handleDragLeave(e) {\n            e.target.closest('.drop-zone').classList.remove('border-green-500', 'bg-green-50');\n        }\n        \n        function handleDrop(e) {\n            e.preventDefault();\n            const dropZone = e.target.closest('.drop-zone');\n            dropZone.classList.remove('border-green-500', 'bg-green-50');\n            \n            const itemId = e.dataTransfer.getData('text/plain');\n            const draggedItem = document.querySelector(`[data-id=\"${itemId}\"]`);\n            \n            if (draggedItem && dropZone) {\n                dropZone.appendChild(draggedItem);\n                dropZone.querySelector('.text-center').style.display = 'none';\n            }\n        }\n        \n        // Check answers functionality\n        checkAnswersBtn.addEventListener('click', () => {\n            // Implementation for checking answers would go here\n            feedbackArea.classList.remove('hidden');\n            feedbackContent.innerHTML = '<p class=\"text-green-600 text-left\">Answers checked! Review your results above.</p>';\n        });",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "4",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "2",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "1",
        "image_description": ""
      },
      {
        "fragment_index": 6,
        "text_description": "5",
        "image_description": ""
      },
      {
        "fragment_index": 7,
        "text_description": "Rise 2, m = 1/2",
        "image_description": ""
      },
      {
        "fragment_index": 8,
        "text_description": "Rise 4, m = 2",
        "image_description": ""
      },
      {
        "fragment_index": 9,
        "text_description": "Rise -3, m = -3",
        "image_description": ""
      },
      {
        "fragment_index": 10,
        "text_description": "Rise 5, m = 1",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 7,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Meet the Intercepts",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "x-Intercept\nPoint where the line cuts the x-axis.\nLies on \\(y = 0\\).\nWritten as \\((a, 0)\\).",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "y-Intercept\nPoint where the line cuts the y-axis.\nLies on \\(x = 0\\).\nWritten as \\((0, b)\\).",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Key Similarities\nBoth are points where the line meets an axis.\nA straight line has one of each.\nHelp sketch the graph quickly.\nValues found by setting the other variable to zero.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 8,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "y = mx + c",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "\\[y = mx + c\\]",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Variable Definitions\n\\(m\\)\ngradient (slope)\n\\(c\\)\ny-intercept \\( (0,c) \\)\n\\(x\\)\nhorizontal coordinate\n\\(y\\)\nvertical coordinate",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Applications",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Quick Sketch\nPlot \\(c\\) on the y-axis, move with slope \\(m\\), draw the straight line.",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "Model Checking\nIdentify slope and intercept to test if data fits a straight-line equation.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 9,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Full Picture",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/sDn7keXqkYFAjx0mCvRGuBlMIKmeE8VRaAcPN8Sc.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Line \\(y = -0.5x + 3\\)\nRead the equation to pick out each intercept and the slope.\nThese values let you quickly place the line on the graph.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Key Points:\nGradient \\(m = -0.5\\)  (negative)\ny-intercept: set \\(x = 0\\) → point \\((0, 3)\\)\nx-intercept: set \\(y = 0\\) → solve \\(0 = -0.5x + 3\\) gives \\(x = 6\\); point \\((6, 0)\\)",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 10,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Multiple Choice Question\nCorrect!\nGreat job—your gradient calculation is accurate.\nIncorrect\nCheck the change in \\(y\\) and \\(x\\) carefully and try again.\nconst correctOption = 0;\n        const answerCards = document.querySelectorAll('.answer-card');\n        const submitBtn = document.getElementById('slide-10-k3g9pv-submitBtn');\n        const feedbackCorrect = document.getElementById('slide-10-k3g9pv-feedbackCorrect');\n        const feedbackIncorrect = document.getElementById('slide-10-k3g9pv-feedbackIncorrect');\n        \n        let selectedOption = null;\n        \n        answerCards.forEach((card, index) => {\n            card.addEventListener('click', () => {\n                answerCards.forEach(c => c.classList.remove('border-blue-500', 'bg-blue-50'));\n                card.classList.add('border-blue-500', 'bg-blue-50');\n                selectedOption = index;\n            });\n        });\n        \n        submitBtn.addEventListener('click', () => {\n            if (selectedOption === null) return;\n            \n            if (selectedOption === correctOption) {\n                feedbackCorrect.classList.remove('hidden');\n                feedbackIncorrect.classList.add('hidden');\n            } else {\n                feedbackIncorrect.classList.remove('hidden');\n                feedbackCorrect.classList.add('hidden');\n            }\n        });",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Question\nWhat is the gradient of the line through \\( (2,1) \\) and \\( (6,5) \\)?",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "1\n1",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "2\n2",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "3\n4",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "4\n\\( \\frac{1}{2} \\)",
        "image_description": ""
      },
      {
        "fragment_index": 6,
        "text_description": "Hint:\nUse \\( m = \\frac{y_2 - y_1}{x_2 - x_1} \\).",
        "image_description": ""
      },
      {
        "fragment_index": 7,
        "text_description": "Submit Answer",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 11,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Key Takeaways\nThank You!\nWe hope you found this lesson informative and engaging.",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Gradient (slope) equals rise / run and shows a line’s steepness.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "The y-intercept is the point where the line meets the y-axis \\((x = 0)\\).",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "The x-intercept is where the line crosses the x-axis \\((y = 0)\\).",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Equation \\(y = mx + c\\) links gradient \\(m\\) and y-intercept \\(c\\) in one formula.",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "Knowing \\(m\\) and the intercepts lets you sketch or interpret any straight line quickly.",
        "image_description": ""
      }
    ]
  }
]