Graphing linear equations examples using intercepts method

📚 Quick Study Guide

💡
• Intercepts: The points where a line crosses the x-axis (x-intercept) and the y-axis (y-intercept).
➗
• Finding the x-intercept: Set $y = 0$ in the equation and solve for $x$. This gives you the point $(x, 0)$.
➕
• Finding the y-intercept: Set $x = 0$ in the equation and solve for $y$. This gives you the point $(0, y)$.
✍️
• Graphing the line: Plot the x-intercept and the y-intercept on the coordinate plane. Draw a straight line through these two points.
➗
• Linear Equation Form: A linear equation can be written in the form $Ax + By = C$, where $A$, $B$, and $C$ are constants.
🧭
• Example: Graphing $2x + 3y = 6$:
  * Set $y = 0$: $2x + 3(0) = 6 \Rightarrow 2x = 6 \Rightarrow x = 3$. X-intercept is $(3, 0)$. * Set $x = 0$: $2(0) + 3y = 6 \Rightarrow 3y = 6 \Rightarrow y = 2$. Y-intercept is $(0, 2)$. * Plot $(3, 0)$ and $(0, 2)$ and draw the line.

Practice Quiz

1. What is the y-intercept of the line $x + y = 5$?
1. (5, 0)
2. (0, 5)
3. (0, -5)
4. (-5, 0)
2. What is the x-intercept of the line $2x - y = 4$?
1. (0, -4)
2. (2, 0)
3. (-2, 0)
4. (0, 4)
3. The line $3x + 4y = 12$ crosses the y-axis at which point?
1. (4, 0)
2. (0, 3)
3. (3, 0)
4. (0, 4)
4. What are the x and y intercepts of the line $5x - 2y = 10$?
1. x-intercept: (2, 0), y-intercept: (0, -5)
2. x-intercept: (5, 0), y-intercept: (0, -2)
3. x-intercept: (0, -5), y-intercept: (2, 0)
4. x-intercept: (0, -2), y-intercept: (5, 0)
5. Which intercept method equation is used to find the y-intercept?
1. Set y = 0
2. Set x = 1
3. Set x = 0
4. Set y = 1
6. What is the x-intercept of the equation $y = 7x + 14$?
1. (2, 0)
2. (-2, 0)
3. (0, 14)
4. (0, -14)
7. Given the intercepts (4, 0) and (0, -3), what linear equation represents the line?
1. $3x - 4y = 12$
2. $3x + 4y = 12$
3. $-3x + 4y = 12$
4. $-3x - 4y = 12$