| --- |
| 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. |
