Equations and Graphs

What are the coordinates of the point where y = 2x + 3 crosses the y-axis?

• A(3, 0)
• B(0, 2)
• C(2, 3)
• D(0, 3)✓

Answer: The line crosses the y-axis when x = 0. Substituting: y = 2(0) + 3 = 3. So the point is (0, 3).

Which of these lines is parallel to y = 2x + 5?

• Ay = 5x + 2
• By = -2x + 5
• Cy = x + 2
• Dy = 2x - 3✓

Answer: Parallel lines have the same gradient. The gradient of y = 2x + 5 is 2, so a parallel line must also have gradient 2, whatever its y-intercept.

What is the equation of the line with gradient 2 and y-intercept -4?

• Ay = 2x + 4
• By = 2x - 4✓
• Cy = -2x - 4
• Dy = 4x + 2

Answer: Using y = mx + c where m = 2 and c = -4: y = 2x - 4.

Find the gradient of the line through points (1, 2) and (3, 8).

• A2
• B3✓
• C4
• D6

Answer: Gradient = (8 - 2) ÷ (3 - 1) = 6 ÷ 2 = 3.

Which of these points lies on the line y = 2x - 1?

• A(1, 3)
• B(3, 5)✓
• C(2, 5)
• D(0, 1)

Answer: Substitute each x-value into y = 2x - 1. When x = 3, y = 2 × 3 - 1 = 5, so the point (3, 5) lies on the line.

A distance-time graph shows a straight line from (0, 0) to (5, 100). What is the speed?

• A20 m/s✓
• B100 m/s
• C50 m/s
• D5 m/s

Answer: Speed = distance / time = 100 / 5 = 20 m/s.

A distance-time graph is horizontal. What does this indicate?

• AAccelerating
• BDecelerating
• CConstant speed
• DNo movement✓

Answer: A horizontal line means distance is not changing, so there is no movement (speed = 0).

A distance-time graph has a steep line then a horizontal line. What happened?

• AConstant speed then stopped✓
• BStopped then accelerated
• CDecelerated then stopped
• DAccelerated then decelerated

Answer: A steep line indicates motion (non-zero speed). A horizontal line indicates no movement. So there was motion, then the object stopped.

A velocity-time graph shows a straight line with positive gradient. What does this indicate?

• AConstant speed
• BNo movement
• CDeceleration
• DAcceleration✓

Answer: A positive gradient in a velocity-time graph indicates acceleration (velocity is increasing).

A real-life graph shows the temperature throughout the day: starting at 10°C in the morning, rising to 20°C by afternoon, then cooling to 15°C by evening. Which graph shape matches this?

• AStraight line decreasing
• BDecreasing then increasing
• CIncreasing then decreasing✓
• DStraight line increasing

Answer: Temperature rises (increases) then falls (decreases), giving a shape that goes up then down.

A linear graph has the equation 3y = 6x + 9. What is the gradient?

• A1
• B2✓
• C3
• D6

Answer: 3y = 6x + 9. Divide by 3: y = 2x + 3. The gradient (m) is 2.