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Linear Equations y=mx+c

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Linear Equations y=mx+c worksheet preview

Linear Equations y=mx+c

Linear graph illustration

📚 Part 1: Understanding y = mx + c

1. In the equation y = 3x + 5, what is the gradient (m)?

3

5

x

y

2. In the equation y = -2x + 7, what is the y-intercept (c)?

-2

2

7

-7

3. Which of these equations represents a line with a negative gradient?

y = 4x + 1

y = -3x + 2

y = x + 6

y = 2x - 5

4. A line passes through the point (0, 4). What is the y-intercept?

Answer: ________________

✏️ Part 2: Finding Gradients and Equations

5. Calculate the gradient of a line that passes through points (1, 3) and (3, 7).

Remember: Gradient = rise ÷ run = (y₂ - y₁) ÷ (x₂ - x₁)

Gradient = ________________

6. A line has gradient 2 and y-intercept -3. Write the equation of this line.

Equation: y = ________________

7. Look at this table of values for a straight line:
x 0 1 2 3
y 1 4 7 10

a) What is the y-intercept? ________________

b) What is the gradient? ________________

c) Write the equation: y = ________________

🚖 Part 3: Real-Life Applications

8. A taxi company charges using the formula: Cost (£) = 2.50 × distance (miles) + 3

a) What does the number 3 represent?

b) What does the number 2.50 represent?

c) How much would a 6-mile journey cost?

Cost = £________________

9. The temperature in a freezer is modelled by: T = -5h + 20

Where T is temperature (°C) and h is hours since the freezer was switched on.

a) What was the starting temperature? ________________°C

b) By how much does the temperature drop each hour? ________________°C

c) What will the temperature be after 3 hours?

Temperature = ________________°C

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