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Graphing Linear Equations
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Graphing Linear Equations
📊 Part 1: Understanding Linear Equations
1. Which of the following is the correct form of a linear equation?
y = mx + c
y = x²
y = 2x³ + 1
y = 5/x
2. In the equation y = 3x + 2, what is the gradient (slope)?
2
3
x
y
3. In the equation y = -x + 5, what is the y-intercept?
-1
1
5
x
4. Which characteristics describe a linear graph? (Select all that apply)
Forms a straight line
Has a constant gradient
Curves upward
Crosses the y-axis at one point
📐 Part 2: Plotting Points and Graphing
5. For the equation y = 2x + 1, complete the table of values:
When x = -1, y = _______
When x = 0, y = _______
When x = 1, y = _______
When x = 2, y = _______
6. Use the coordinate grid below to plot the points from question 5 and draw the line for y = 2x + 1:
7. For the equation y = -x + 3, find three coordinate points and show your working:
8. Looking at the graph of y = 0.5x - 2, explain what happens to the line when the gradient is a fraction:
🎯 Part 3: Analysis and Real-World Connections
9. A mobile phone plan costs $20 per month plus $0.50 for each text message. Write this as a linear equation where y = total cost and x = number of text messages:
y = _____________
10. Explain in your own words how changing the gradient (m) in y = mx + c affects the appearance of the line on a graph:
11. Two lines have equations y = 2x + 1 and y = 2x - 3. Without graphing, explain what you know about these lines:
12. Challenge: If a line passes through points (0, 4) and (2, 8), what is its equation? Show your working:
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