source: ncert
topic: algebra
class_level: class_8
chapter: ch15
difficulty: beginner
Class 8 | Ch15: Introduction to Graphs TYPES OF GRAPHS: Bar graph: compares discrete data using bars. Line graph: shows change over time (continuous data). Pie chart: shows proportions (parts of a whole). Histogram: bar graph for continuous grouped data (no gaps). LINEAR GRAPHS: Equation of straight line: y=mx+c where m=slope, c=y-intercept. x-intercept: point where line crosses x-axis (y=0). y-intercept: point where line crosses y-axis (x=0). Slope m: if line passes through (x1,y1) and (x2,y2): m=(y2-y1)/(x2-x1). PLOTTING POINTS AND GRAPHS: For any linear equation, find at least 2 points (3 to verify). For x+y=5: when x=0,y=5. When x=5,y=0. When x=2,y=3. Plot these points and join with straight line. READING GRAPHS: Distance-time graph: slope=speed. Horizontal line=stationary. Steep line=fast. Temperature-time graph: shows heating/cooling patterns. APPLICATIONS: Finding values from graph (interpolation and extrapolation). Conversion graphs: between units (km to miles, °C to °F). SOLVED EXAMPLES: Example 1: Draw graph of y=2x+1. Plot (-1,-1), (0,1), (1,3). Join them. Example 2: For graph x+2y=6, find x and y intercepts. x-intercept (y=0): x=6. y-intercept (x=0): y=3. Example 3: Plot points A(2,3), B(-1,4), C(0,-2). A: right 2, up 3. B: left 1, up 4. C: at origin, down 2. Example 4: Distance-time graph, car goes 60km in 1 hour. Speed=60/1=60kmph. COMMON MISTAKES: x-intercept: set y=0 (NOT x=0). y-intercept: set x=0. Plotting: x-coordinate first (horizontal), then y-coordinate (vertical). In distance-time graph, slope=speed. Greater slope=greater speed.