Easy examples of graphing lines using slope and y-intercept

📚 Quick Study Guide

• 📈 Slope-Intercept Form: The equation of a line is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• 📍 Y-Intercept: The y-intercept is the point where the line crosses the y-axis. It occurs when $x = 0$. In the equation $y = mx + b$, $b$ represents the y-coordinate of the y-intercept (0, b).
• ⛰️ Slope: The slope ($m$) represents the rate of change of the line. It is calculated as rise over run: $m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}$. A positive slope indicates an increasing line, while a negative slope indicates a decreasing line.
• ✍️ Graphing Steps:
  1. 📌 Identify the y-intercept ($b$) and plot the point (0, b) on the y-axis.
  2. 🧭 Use the slope ($m$) to find another point. Write $m$ as a fraction. The numerator is the 'rise' (vertical change), and the denominator is the 'run' (horizontal change).
  3. ✏️ Starting from the y-intercept, move according to the rise and run to plot the second point.
  4. 📏 Draw a straight line through the two points.

🧪 Practice Quiz

1. What is the slope of the line $y = 3x - 2$?
1. A. -2
2. B. 2/3
3. C. 3
4. D. -3
2. What is the y-intercept of the line $y = -2x + 5$?
1. A. -2
2. B. 5
3. C. 2
4. D. -5
3. A line has a slope of 2 and a y-intercept of -1. What is the equation of the line?
1. A. $y = -x + 2$
2. B. $y = 2x - 1$
3. C. $y = -x - 1$
4. D. $y = x + 2$
4. What point does the line $y = x + 3$ intersect the y-axis?
1. A. (3, 0)
2. B. (0, -3)
3. C. (0, 3)
4. D. (-3, 0)
5. If a line has a slope of -1/2 and passes through the point (0, 4), what is the equation of the line?
1. A. $y = 4x - \frac{1}{2}$
2. B. $y = -\frac{1}{2}x + 4$
3. C. $y = \frac{1}{2}x - 4$
4. D. $y = -4x + \frac{1}{2}$
6. Which of the following lines is parallel to $y = 2x + 3$?
1. A. $y = -2x + 1$
2. B. $y = \frac{1}{2}x + 3$
3. C. $y = 2x - 5$
4. D. $y = -\frac{1}{2}x + 3$
7. A line passes through the points (0, 2) and (1, 5). What is the slope of the line?
1. A. 2
2. B. 3
3. C. 4
4. D. 5