Cambridge IGCSE · Mathematics (0580)

Gradient of linear graphs: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Gradient of linear graphs.

10 questions23 marksFree, no account

Question 1

1 mark

A straight line passes through the points \(A(3, 2)\) and \(B(9, 6)\).
Determine the gradient of this line.

Question 2

1 mark

Find the gradient of the straight line that passes through the points \(A(-5, 2)\) and \(B(1, -10)\).

Question 3

1 mark

A straight line passes through point \(P(k, 2k)\) and point \(Q(5, 11)\).
Given that the gradient of the line is \(3\), find the value of \(k\).

Question 4

1 mark

A straight line is plotted on a coordinate grid. For every 1 unit the line moves to the right horizontally, it moves 3 units upwards vertically. Determine the gradient of this line.

Question 5

1 mark

The line passing through \(P(k, 4)\) and \(Q(5, 10)\) has a gradient of \(2\).
Find the value of \(k\).

Question 6

2 marks

Determine the gradient of the straight line that passes through the points with coordinates \((0, 8)\) and \((4, 0)\).

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Determine the gradient of the straight line that passes through the coordinates \(A(-4, -2)\) and \(B(2, 10)\).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Calculate the gradient of a line that is perpendicular to the line with equation \(3x + 4y = 12\).

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Question 9

3 marks

A straight line is drawn on a coordinate grid. The line passes through the points A \((1, 2)\) and B \((4, 8)\).

(a) Find the gradient of the line passing through points A and B.

(b) Find the coordinates of the midpoint of the line segment AB.

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

Consider the points A(-2, 5), B(4, 1), and C(7, y) in a Cartesian coordinate system.

(a) Calculate the gradient of the line segment AB.

(b) Find the equation of the line passing through A and B. Give your answer in the form $$y = mx + c$$.

(c) The line segment BC is parallel to the line $$2x + 3y = 10$$. Find the value of y.

Write your answer out first, then check it against the worked solution.

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