Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 13 Graphs

Gradient of a line through two points

Answer: 2

💡 What it's asking: The gradient tells you how steep a line is: how much y changes for each step in x. Use the two points to find the change in y over the change in x.

1. 1Take the first point as (4, 2) and the second as (2, -2).
2. 2Change in y: -2 - 2 = -4.
3. 3Change in x, in the same order: 2 - 4 = -2.
4. 4Gradient = -4 ÷ -2 = 2 (a negative divided by a negative is positive).

✅ Going from (2, -2) to (4, 2), x goes up 2 and y goes up 4, so y rises 2 for every 1 step in x: gradient 2.

Equation of a line through two points

Answer: y = 2x - 5

💡 What it's asking: A straight line's equation is y = mx + c. Find the gradient m from the two points, then use one point to find c.

1. 1Gradient m = (change in y) ÷ (change in x) = (-1 - 3) ÷ (2 - 4) = -4 ÷ -2 = 2.
2. 2So the line is y = 2x + c. We still need c, the y-intercept.
3. 3Put the point (4, 3) in: 3 = 2 × 4 + c, so 3 = 8 + c.
4. 4c = 3 - 8 = -5, so the line is y = 2x - 5.

✅ Try the other point (2, -1): 2 × 2 - 5 = -1. It works, so the equation is right.