{
  "title": "Linear Graphs (Introduction to Graphs) - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What type of graph represents y = 2x + 3? 📈",
      "options": {
        "A": "Straight line",
        "B": "Curve",
        "C": "Parabola",
        "D": "Circle"
      },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "In y = mx + c, what does 'm' represent? 🤔",
      "options": {
        "A": "Y-intercept",
        "B": "Slope",
        "C": "X-intercept",
        "D": "Constant"
      },
      "correct_answer": "B"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is the slope of y = 4x - 1? ↗️",
      "options": { "A": "4", "B": "-1", "C": "1", "D": "0" },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "For y = 3, the graph is a ______ line. ➖",
      "options": {
        "A": "Horizontal",
        "B": "Vertical",
        "C": "Diagonal",
        "D": "Curved"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "What is the y-intercept of y = 2x + 5? 📍",
      "options": { "A": "2", "B": "5", "C": "0", "D": "-5" },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "If slope is 0, the line is ______. 📏",
      "options": {
        "A": "Vertical",
        "B": "Horizontal",
        "C": "45° inclined",
        "D": "Curved"
      },
      "correct_answer": "B"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "What is the graph of x = -2? ↕️",
      "options": {
        "A": "Horizontal line",
        "B": "Vertical line",
        "C": "Diagonal line",
        "D": "Parabola"
      },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Which equation has slope 3? 🎯",
      "options": {
        "A": "y = 3x + 2",
        "B": "y = 2x + 3",
        "C": "y = x + 3",
        "D": "y = 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "The line y = -x + 4 slopes ______. 📉",
      "options": {
        "A": "Upward right",
        "B": "Downward right",
        "C": "Horizontal",
        "D": "Vertical"
      },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "What is the slope of y = 7? 🔄",
      "options": { "A": "7", "B": "1", "C": "0", "D": "Undefined" },
      "correct_answer": "C"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Which point lies on y = 2x? ✨",
      "options": { "A": "(1,2)", "B": "(2,1)", "C": "(0,2)", "D": "(2,0)" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "If y = 3x - 6, what is y when x = 2? 🔢",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "2" },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "A line with positive slope goes ______. ↗️",
      "options": {
        "A": "Upward left",
        "B": "Downward right",
        "C": "Upward right",
        "D": "Horizontal"
      },
      "correct_answer": "C"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "What is the x-intercept of y = x - 3? 📍",
      "options": { "A": "3", "B": "-3", "C": "0", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Which is a linear equation? ✅",
      "options": {
        "A": "y = x²",
        "B": "y = 2x + 1",
        "C": "y = 1/x",
        "D": "y = √x"
      },
      "correct_answer": "B"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "If two lines have same slope, they are ______. 🔄",
      "options": {
        "A": "Perpendicular",
        "B": "Parallel",
        "C": "Intersecting",
        "D": "Curved"
      },
      "correct_answer": "B"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "What is slope of line through (0,0) and (2,4)? 📏",
      "options": { "A": "2", "B": "4", "C": "1/2", "D": "0" },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "The equation y = 5 represents line parallel to ______ axis. ➖",
      "options": { "A": "x-axis", "B": "y-axis", "C": "both", "D": "neither" },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Which line is steeper: y = 10x or y = 2x? 🏔️",
      "options": {
        "A": "y = 10x",
        "B": "y = 2x",
        "C": "Same",
        "D": "Can't tell"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "If y = -2x + 3, what is y-intercept? 📍",
      "options": { "A": "-2", "B": "3", "C": "2", "D": "-3" },
      "correct_answer": "B"
    },

    {
      "id": 21,
      "difficulty": "medium",
      "question": "Find slope of line passing through (1,2) and (4,8). 📐",
      "options": {
        "A": "2",
        "B": "3",
        "C": "1/2",
        "D": "6"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "What is equation of line with slope 2 and y-intercept -3? ✍️",
      "options": {
        "A": "y = 2x - 3",
        "B": "y = 3x + 2",
        "C": "y = 2x + 3",
        "D": "y = -3x + 2"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "If line passes through (0,4) and (2,10), find equation. 📈",
      "options": {
        "A": "y = 3x + 4",
        "B": "y = 4x + 2",
        "C": "y = 2x + 4",
        "D": "y = x + 4"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Which line is perpendicular to y = (1/2)x + 1? ⟂",
      "options": {
        "A": "y = -2x + 3",
        "B": "y = 2x + 1",
        "C": "y = (1/2)x - 2",
        "D": "y = -1/2 x + 1"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Find x-intercept of 3x + 2y = 12. 📍",
      "options": { "A": "4", "B": "6", "C": "3", "D": "12" },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "What is slope of line 4x - 2y = 8? 📏",
      "options": {
        "A": "2",
        "B": "-2",
        "C": "4",
        "D": "1/2"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Line parallel to y = 3x + 5 and passing through (0,0) is? 🔄",
      "options": {
        "A": "y = 3x",
        "B": "y = 5x",
        "C": "y = x + 3",
        "D": "y = 3x + 1"
      },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "If y = kx passes through (2,6), find k. 🔢",
      "options": { "A": "3", "B": "2", "C": "6", "D": "1/3" },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Find equation of line with x-intercept 3 and y-intercept 4. 📐",
      "options": {
        "A": "4x + 3y = 12",
        "B": "3x + 4y = 12",
        "C": "x/3 + y/4 = 1",
        "D": "y = -4/3 x + 4"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "What is slope of line perpendicular to y = -4x + 7? ⟂",
      "options": {
        "A": "1/4",
        "B": "-1/4",
        "C": "4",
        "D": "-4"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Line passing through (1,1) and (3,5) has equation? 📝",
      "options": {
        "A": "y = 2x - 1",
        "B": "y = 3x - 2",
        "C": "y = x + 1",
        "D": "y = 4x - 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "If 2x + 3y = 6, find y when x = 0. 🔄",
      "options": {
        "A": "2",
        "B": "3",
        "C": "6",
        "D": "0"
      },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Which point satisfies 2y = x + 4? ✅",
      "options": { "A": "(0,2)", "B": "(2,0)", "C": "(4,0)", "D": "(0,4)" },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "Slope of line joining (-2,3) and (4,-1) is? 📉",
      "options": {
        "A": "-2/3",
        "B": "2/3",
        "C": "-3/2",
        "D": "3/2"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Find k if (3,k) lies on y = 2x - 5. 🎯",
      "options": {
        "A": "1",
        "B": "2",
        "C": "-1",
        "D": "0"
      },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Equation of line parallel to x-axis passing through (4,-2)? ➖",
      "options": { "A": "y = -2", "B": "x = 4", "C": "y = 4", "D": "x = -2" },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "What is y-intercept of line 5x - y = 10? 📍",
      "options": {
        "A": "-10",
        "B": "10",
        "C": "5",
        "D": "-5"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "If slope is undefined, line is ______. ↕️",
      "options": {
        "A": "Horizontal",
        "B": "Vertical",
        "C": "45° line",
        "D": "Curved"
      },
      "correct_answer": "B"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Find equation of line through origin with slope -1. 🔄",
      "options": { "A": "y = -x", "B": "y = x", "C": "y = -1", "D": "x = -y" },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Line perpendicular to x-axis has slope? ⟂",
      "options": { "A": "0", "B": "1", "C": "Undefined", "D": "-1" },
      "correct_answer": "C"
    },

    {
      "id": 41,
      "difficulty": "hard",
      "question": "Find equation of line through (2,3) perpendicular to y = -1/3 x + 4. 🧠",
      "options": {
        "A": "y = 3x - 3",
        "B": "y = 3x + 3",
        "C": "y = -3x + 9",
        "D": "y = 1/3 x + 7/3"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "If lines 2x + ky = 7 and 3x - 4y = 5 are parallel, find k. 🔄",
      "options": {
        "A": "-8/3",
        "B": "8/3",
        "C": "3/8",
        "D": "-3/8"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Point of intersection of y = 2x + 1 and y = -x + 7 is? 📍",
      "options": { "A": "(2,5)", "B": "(5,2)", "C": "(1,7)", "D": "(3,4)" },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Area of triangle formed by x=0, y=0, and 3x+4y=12 is? 📐",
      "options": { "A": "6", "B": "12", "C": "24", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Line makes intercepts a and b on axes. If a+b=10 and ab=21, find equation. 📏",
      "options": {
        "A": "7x + 3y = 21 or 3x + 7y = 21",
        "B": "5x+5y=25",
        "C": "2x+8y=16",
        "D": "x+y=10"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "If line (k-1)x + (k+1)y = 2 passes through (1,1), find k. 🔢",
      "options": {
        "A": "1",
        "B": "2",
        "C": "0",
        "D": "-1"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Distance between parallel lines y = 2x + 3 and y = 2x - 4? 📏",
      "options": { "A": "7/√5", "B": "3", "C": "4", "D": "√5" },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Find equation of line through intersection of x+y=4, x-y=2 and parallel to 3x+4y=5. 🧩",
      "options": {
        "A": "3x+4y=14",
        "B": "3x+4y=10",
        "C": "4x+3y=14",
        "D": "4x+3y=10"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "If point (a,2a) lies on line 3x - 4y = 5, find a. 🎯",
      "options": { "A": "1", "B": "2", "C": "3", "D": "4" },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Slope of line making 60° with x-axis is? 📐",
      "options": { "A": "√3", "B": "1/√3", "C": "1", "D": "√3/2" },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Line through (1,2) cuts axes at P and Q. If midpoint of PQ is (1,2), find equation. 📍",
      "options": {
        "A": "2x + y = 4",
        "B": "x + 2y = 5",
        "C": "x + y = 3",
        "D": "3x + y = 5"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "If perpendicular from origin to line has slope 2 and length √5, find line equation. 🧠",
      "options": {
        "A": "2x - y = 5",
        "B": "2x + y = 5",
        "C": "x - 2y = 5",
        "D": "x + 2y = 5"
      },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Lines ax+by+c=0 and bx-ay+d=0 are ______. 🔄",
      "options": {
        "A": "Perpendicular",
        "B": "Parallel",
        "C": "Coincident",
        "D": "Intersecting at 45°"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Find equation of line through (3,4) making equal intercepts on axes. ⚖️",
      "options": {
        "A": "x + y = 7",
        "B": "x - y = 1",
        "C": "x + y = 1",
        "D": "x - y = 7"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "If line segment joining (2,3) and (4,7) is extended to (6,k), find k. 📏",
      "options": { "A": "11", "B": "9", "C": "10", "D": "12" },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Line passing through (1,4) and perpendicular to line through (2,3) and (4,5) has equation? ⟂",
      "options": {
        "A": "x + y = 5",
        "B": "x - y = -3",
        "C": "x + y = 3",
        "D": "x - y = 5"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "If three lines x+y=1, x-y=1, and kx+y=3 are concurrent, find k. 📍",
      "options": { "A": "2", "B": "3", "C": "1", "D": "4" },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Distance between line 3x+4y=10 and point (2,1) is? 📏",
      "options": { "A": "12/5", "B": "5/12", "C": "3", "D": "4" },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Find equation of line through (4,5) and cutting off equal positive intercepts on axes. ✨",
      "options": {
        "A": "x + y = 9",
        "B": "x - y = -1",
        "C": "x + y = 1",
        "D": "x - y = 9"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "If line y = mx + c passes through (1,1) and (2,3), find m and c. 🔢",
      "options": {
        "A": "m=2, c=-1",
        "B": "m=1, c=0",
        "C": "m=3, c=-2",
        "D": "m=2, c=1"
      },
      "correct_answer": "A"
    }
  ]
}