Simple linear equations and their graph examples

📚 Quick Study Guide

• 🔢 A linear equation is an equation between two variables that gives a straight line when plotted on a graph.
• 📈 The standard form of a linear equation is $y = mx + b$, where:
  • $m$ represents the slope of the line.
  • $b$ represents the y-intercept (the point where the line crosses the y-axis).
• ➕ To graph a linear equation:
  • Choose a few values for $x$.
  • Substitute these values into the equation to find the corresponding $y$ values.
  • Plot the points $(x, y)$ on a coordinate plane.
  • Draw a straight line through the points.
• 🧭 The slope ($m$) can be calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
• 📍 The y-intercept ($b$) is the value of $y$ when $x = 0$.

Practice Quiz

1. What is the slope of the line represented by the equation $y = 3x + 5$?
1. A) 1
2. B) 3
3. C) 5
4. D) 8
2. Which of the following equations represents a line with a y-intercept of -2?
1. A) $y = x + 2$
2. B) $y = x - 2$
3. C) $y = 2x$
4. D) $y = -2x$
3. What is the equation of a line that passes through the points (0, 1) and (1, 3)?
1. A) $y = x + 1$
2. B) $y = 2x + 1$
3. C) $y = 3x$
4. D) $y = x + 3$
4. If a line has a slope of -2 and passes through the point (1, 4), what is its equation?
1. A) $y = -2x + 6$
2. B) $y = -2x + 4$
3. C) $y = 2x + 6$
4. D) $y = -2x + 2$
5. Which of the following points lies on the line $y = 4x - 3$?
1. A) (1, 2)
2. B) (2, 4)
3. C) (0, 3)
4. D) (-1, -7)
6. What is the y-intercept of the line $2y = 4x + 6$?
1. A) 2
2. B) 3
3. C) 4
4. D) 6
7. A line is parallel to $y = 5x - 2$. Which of the following could be its equation?
1. A) $y = -5x + 1$
2. B) $y = \frac{1}{5}x + 3$
3. C) $y = 5x + 4$
4. D) $y = -\frac{1}{5}x - 2$