Quiz on graphing lines using slope-intercept form

📚 Quick Study Guide

• 🔢 The Slope-Intercept Form: The equation of a line is expressed as $y = mx + b$, where:
• 📈 $m$ represents the slope of the line.
• 📍 $b$ represents the y-intercept (the point where the line crosses the y-axis).
• 🧭 Slope ($m$): Slope measures the steepness of a line. It's calculated as "rise over run," or $\frac{\text{change in } y}{\text{change in } x}$. A positive slope indicates an increasing line, while a negative slope indicates a decreasing line.
• 📌 Y-Intercept ($b$): The y-intercept is the point $(0, b)$ where the line intersects the y-axis. To find it, set $x = 0$ in the equation and solve for $y$.
• ✏️ 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 on the line. Remember, $m = \frac{\text{rise}}{\text{run}}$. From the y-intercept, move up or down according to the rise and right according to the run.
  3. 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. 3
3. C. 1
4. D. -3


2. What is the y-intercept of the line $y = -x + 5$?
1. A. -1
2. B. 5
3. C. 0
4. D. -5


3. Which of the following lines has a slope of 2 and a y-intercept of -1?
1. A. $y = -x + 2$
2. B. $y = 2x - 1$
3. C. $y = -2x + 1$
4. D. $y = x - 2$


4. What is the equation of a line with a slope of -1/2 and a y-intercept of 3?
1. A. $y = 3x - \frac{1}{2}$
2. B. $y = -\frac{1}{2}x + 3$
3. C. $y = \frac{1}{2}x - 3$
4. D. $y = -3x + \frac{1}{2}$


5. The line $y = 4x + b$ passes through the point (0, -2). What is the value of $b$?
1. A. 4
2. B. -2
3. C. 0
4. D. 2


6. Which equation represents a horizontal line passing through the point (0, 5)?
1. A. $x = 5$
2. B. $y = x + 5$
3. C. $y = 5$
4. D. $x = y + 5$


7. A line has a slope of -2 and passes through the point (1, 1). What is its equation in slope-intercept form?
1. A. $y = -2x + 3$
2. B. $y = 2x - 1$
3. C. $y = -2x - 1$
4. D. $y = -x + 2$