Linear Graphs Worksheet

Name:

Date:

📚 Part 1: Key Concepts

Linear Equation: An equation in the form y = mx + c, where m is the gradient and c is the y-intercept.

Gradient (m): The steepness of the line. Rise over run (vertical change ÷ horizontal change).

Y-intercept (c): The point where the line crosses the y-axis.

1. For the equation y = 3x + 2, what is the gradient?

2. For the equation y = -4x + 7, what is the y-intercept?

-4

(0, 7)

3. Which of the following equations represent linear relationships? (Select all that apply)

y = 2x + 5

y = x²

y = -3x

y = 4

📈 Part 2: Drawing Linear Graphs

Step-by-Step Method:

1. Identify the y-intercept (c) and plot this point on the y-axis
2. Use the gradient (m) to find another point
3. Draw a straight line through both points

4. For y = 2x - 3, complete the steps:

a) Y-intercept: (0, _____)

b) Starting from the y-intercept, move up _____ and right _____ to find the next point.

c) Second point coordinates: (1, _____)

5. Draw the graph of y = -½x + 4 on the grid below. Show your working.

6. For the equation y = 3x + 1:

a) Y-intercept: __________

b) Gradient: __________

c) When x = 2, y = __________

d) When y = 10, x = __________

✏️ Part 3: Problem Solving

7. A mobile phone plan costs $25 per month plus $0.50 per text message. Write a linear equation where y is the total cost and x is the number of text messages.

Equation: y = __________

8. The temperature in a freezer starts at 20°C and decreases by 3°C every hour.

a) Write an equation for temperature (T) after h hours: T = __________

b) What will the temperature be after 5 hours? __________

c) After how many hours will the temperature reach -10°C? __________

9. Explain in your own words how to use the gradient to find a second point when graphing a linear equation.