Equation of a straight line

Maths year 10/11: gradients, intercepts and equations of straight lines

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What is a graph » More

A treasure map tells you how to get to the treasure.

From a start point it tells you how many steps you need to go in each direction.

On this map from the start you need to go 5 steps along to the right and then 3 steps up.

Graph paper is just a grid of squares.

You draw a horizontal and a vertical line on the paper which cross at a point called the origin.

You need an origin because you can go along left and right and go up and down like on the map.

graph paper

Sometimes they say go along the corridor and up the stairs.

The vertical scale is called the Y axis. Remember the vertical part of the Y.

The horizontal scale is called ther X axis.

Q: If you started at point A on the map what are the steps to reach the treasure


What is a co-ordinates  Menu

Every point on the grid can be found with two numbers.

One along the vertical scale labelled y and one on the horizontal scale labelled x

These are called co-ordinates and written like (x , y) where x and y are numbers.

The origin is the point (0, 0)

On the grid shown, (1,2) is one along the x scale right from zero and two along the y scale up from zero.


Q: What are the co-ordinates of the other points


Straight lines  Menu

A straight line is one that does not curve.

It is the shortest distance between two points.

A straight line that goes through a set of co-ordinates has an equation

Look at the vertical line that goes through (2, -1), (2, 0) and (2, 3). All the x co-ordinates are 2. This line has the equation x = 2

Q1: What is the equation of the horizontal line?


Straight lines - gradients Menu  » More

Look at these lines on the grid

line equation

What do you notice about the co-ordinates on the red line?

The co-ordinates are (–1, –1), (1, 1), (2, 2) and (3, 3)

So the x-co-ordinates are the same as the y co-ordinates.

We write this as y = x and say the equation of this line is y = x.

The gradient of a line is how much it goes up or down in a certain horizontal distance

Gradient is how steep a line is.

Use a triangle to work out a gradient as shown above. Divide the height by the width (3 ÷ 3 = 1)

So the gradient of the red line is 1.

Q1: What is the equation of the blue line.

Q2: What is the gradient of the blue line.


Q3: What is this gradient:

Q4: What is this gradient:


Q5: What does the line look like with a gradient of 0.

Q6: What does the line look like with a gradient of infinity.


Straight lines - intercepts  Menu

The intercept is where the line crosses the y or the x axis

Q: What is the intercept for a line with equation y = x.


Straight lines - equations  Menu

The equation of a straight line is: y=mx+c

where m is the gradient and c is the intercept. (in some countries it's b not c

This is the y-intercept and is the y value at that point

Looking at this line, the gradient, m = 1
and the intercept c (the y value) = 2

So the equation of this line is y = x + 2

equation straight line

Q1: What is the equation of line A and line B

Q2: Do you notice anything about these lines