c c x 0 2 4 6 y 1 2 3 4 . The table is for the relation y = mx + c where m and c are constants. What is the…

Analyze the question: The table gives points on a straight line y = mx + c. We need to find m (gradient) and c (y-intercept).

Concept: For a line y = mx + c:

• c is the value of y when x = 0
• m = (change in y) ÷ (change in x)

Solution:

1. When x = 0, y = 1, so c = 1.

2. Gradient using the points (0, 1) and (2, 2): m = (2 − 1) ÷ (2 − 0) = 1/2

3. So the equation is y = ½x + 1.

Check with the other points:

• x = 4: y = ½(4) + 1 = 3 ✓
• x = 6: y = ½(6) + 1 = 4 ✓

Eliminating the other options:

• A. y = 2x gives y = 0 at x = 0, but the table says 1 ✗
• B. y = x + 1 gives y = 3 at x = 2, but the table says 2 ✗
• C. y = x gives y = 0 at x = 0 ✗

Tip: In a table question, always check x = 0 first. It gives you c immediately. Then use any other point to find m, and test the remaining points to confirm. Notice also that x goes up by 2 each time while y goes up by 1, so the gradient is 1/2.