Solved Examples: Graphing Linear Equations in Slope-Intercept Form

📚 Quick Study Guide

• 📈 Slope-Intercept Form: A linear equation in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.
• 📍 Slope ($m$): The rate of change of $y$ with respect to $x$. It indicates the steepness and direction of a line. Calculated as rise over run: $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$.
• 🌠 Y-Intercept ($b$): The point where the line crosses the y-axis. The coordinates of the y-intercept are $(0, b)$.
• ✍️ Graphing Steps:
  1. Plot the y-intercept $(0, b)$ on the y-axis.
  2. Use the slope $m$ to find another point. If $m = \frac{a}{b}$, move $a$ units vertically and $b$ units horizontally from the y-intercept.
  3. Draw a straight line through the two points.
• ➕ Positive Slope: The line rises from left to right.
• ➖ Negative Slope: The line falls from left to right.
• ↔️ Zero Slope: The line is horizontal ($y = b$).
• ↕️ Undefined Slope: The line is vertical ($x = a$).

Practice Quiz

1. What is the slope of the line $y = 3x - 2$?
1. 3
2. -2
3. 1
4. 0


2. What is the y-intercept of the line $y = -2x + 5$?
1. (0, -2)
2. (0, 5)
3. (5, 0)
4. (-2, 5)


3. Which point lies on the line $y = x + 1$?
1. (1, 1)
2. (0, 0)
3. (2, 3)
4. (-1, -1)


4. What is the equation of a line with a slope of 2 and a y-intercept of -3?
1. $y = -3x + 2$
2. $y = 2x - 3$
3. $y = -2x + 3$
4. $y = 3x - 2$


5. What is the slope of the line $y = 7$?
1. 7
2. 1
3. 0
4. Undefined


6. Which of the following lines is parallel to $y = 4x - 1$?
1. $y = -4x + 2$
2. $y = \frac{1}{4}x - 3$
3. $y = 4x + 5$
4. $y = -\frac{1}{4}x + 1$


7. What is the y-intercept of the line $3y = 6x + 9$?
1. (0, 2)
2. (0, 3)
3. (0, 6)
4. (0, 9)