Finding Line Equations Worksheet

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Date:

📚 Part 1: Understanding Linear Equations

Key Formula: The equation of a straight line is y = mx + c, where:

• m = gradient (slope) = rise/run = (y₂ - y₁)/(x₂ - x₁)

• c = y-intercept (where the line crosses the y-axis)

1. A line passes through points (2, 5) and (4, 11). Calculate the gradient.

2. If a line has gradient m = 3 and passes through point (1, 7), find the equation of the line.

3. Multiple Choice: What is the y-intercept of the line y = -2x + 8?

-2

-8

Method: 1) Find gradient using m = (y₂ - y₁)/(x₂ - x₁) 2) Substitute into y = mx + c using one point 3) Solve for c

4. Find the equation of the line passing through (-1, 3) and (2, 9).

5. A line passes through (0, -4) and (3, 2). Write the equation in the form y = mx + c.

6. Extension Challenge: Find the equation of the line passing through (-2, 5) and (4, -7). Then determine where this line intersects the x-axis.

7. A mobile phone plan costs $30 per month plus $0.50 per GB of data used. Write an equation for the total cost (C) in terms of data used (d GB).

8. Differentiated Task: Choose your level:

Level A (Foundation): Find the equation of a line with gradient 4 that passes through (0, 7).

Level B (Standard): Find the equation of a line passing through (1, 5) and (3, 13).

Level C (Advanced): Two lines are parallel. One passes through (2, 3) and (5, 12). The other passes through (0, 1). Find both equations.

9. Success Criteria Check: Tick what you can do confidently:

Calculate gradient from two points

Find y-intercept from a graph or equation

Write equations in y = mx + c form

Apply linear equations to real-world problems