Sec 3 E-Math · Coordinate geometry

Gradient questions with answers

Practice questions on gradient, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

Find the gradient of the line joining $A(4, 3)$ and $B(6, -3)$ .

Step 1 of 2

Put the coordinates into the gradient formula

m = \dfrac{y_2 - y_1}{x_2 - x_1}

m = \dfrac{-3 - 3}{6 - 4}

Try a question: Gradient

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Questions

Question 1Two points, whole-number gradient
Find the gradient of the line joining $A(-1, -2)$ and $B(1, 2)$ .
Show the worked solution
1. Step 1: Put the coordinates into the gradient formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ $m = \dfrac{2 - (-2)}{1 - (-1)}$
2. Step 2: Work it out and simplify $m = \dfrac{4}{2}$ $\phantom{m} = 2$
Question 2Fraction gradients
Find the gradient of the line joining $A(4, -2)$ and $B(-4, -3)$ .
Show the worked solution
1. Step 1: Put the coordinates into the gradient formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ $m = \dfrac{-3 - (-2)}{-4 - 4}$
2. Step 2: Work it out and simplify $m = \dfrac{-1}{-8}$ $\phantom{m} = \dfrac{1}{8}$
Question 3From an equation
Find the gradient of the line $6x + y = 10$ .
Show the worked solution
1. Step 1: Make y the subject $y = -6x + 10$
2. Step 2: The gradient is the number in front of x $m = -6$
Question 4Find a missing coordinate
The line passing through $A(-4, k)$ and $B(-3, -5)$ has gradient $-2$ . Find $k$ .
Show the worked solution
1. Step 1: Write the gradient with k in it $\dfrac{-5 - k}{-3 - (-4)} = -2$
2. Step 2: Solve for k $-5 - k = -2$ $k = -3$

More on coordinate geometry

Notes: Coordinate geometry Worksheet with answers (PDF)

Endless questions on gradient

A free account gives you new questions every time, step-by-step help, and tracks what you've mastered.

Start free

Worked example

Find the gradient of the line joining

A(4, 3)

and

B(6, -3)

Step 1 of 2

Put the coordinates into the gradient formula

m = \dfrac{y_2 - y_1}{x_2 - x_1}

m = \dfrac{-3 - 3}{6 - 4}

Questions

Question 1Two points, whole-number gradient

Find the gradient of the line joining $A(-1, -2)$ and $B(1, 2)$ .

Show the worked solution

Step 1: Put the coordinates into the gradient formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ $m = \dfrac{2 - (-2)}{1 - (-1)}$
Step 2: Work it out and simplify $m = \dfrac{4}{2}$ $\phantom{m} = 2$

Question 2Fraction gradients

Find the gradient of the line joining $A(4, -2)$ and $B(-4, -3)$ .

Show the worked solution

Step 1: Put the coordinates into the gradient formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ $m = \dfrac{-3 - (-2)}{-4 - 4}$
Step 2: Work it out and simplify $m = \dfrac{-1}{-8}$ $\phantom{m} = \dfrac{1}{8}$

Question 3From an equation

Find the gradient of the line $6x + y = 10$ .

Show the worked solution

Step 1: Make y the subject $y = -6x + 10$
Step 2: The gradient is the number in front of x $m = -6$

Question 4Find a missing coordinate

The line passing through $A(-4, k)$ and $B(-3, -5)$ has gradient $-2$ . Find $k$ .

Show the worked solution

Step 1: Write the gradient with k in it $\dfrac{-5 - k}{-3 - (-4)} = -2$
Step 2: Solve for k $-5 - k = -2$ $k = -3$