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Straight line graphs

Straight line graphs

Straight line graphs

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Tutor: Toby

Summary

Straight line graphs

​​In a nutshell

Straight lines join two points on a coordinate grid together and can continue past those points infinitely. There are three types of straight line graphs: horizontal, vertical and diagonal. Straight lines can be described using two quantities: the gradient and the yy-intercept.


Definitions

Gradient

How steep the line is. 

y-INTERCEPT

The point on the yy-axis where the line crosses through.​

Horizontal

A straight line going between left and right. Think of the "horizon" to help you remember.

Vertical

A straight line going between up and down.


​​Different gradients

You need to be able to recognise if a line has a positive, negative or zero gradient. You can denote the gradient with mm.​


Positive gradient

If a line has a positive gradient, then it is a diagonal line, moving up as it moves to the right. The line below has a positive gradient, or in other words, m>0m>0​:

Maths; Straight line graphs; KS3 Year 7; Straight line graphs

The bigger the value of mm, the steeper the line. So a line with gradient 55 is steeper than a line with gradient 22.​


​​Negative gradient

A line with a negative gradient is also a diagonal line, but it moves down as it moves to the right. The line below has a negative gradient. In other words, m<0m<0​:

Maths; Straight line graphs; KS3 Year 7; Straight line graphs

The more negative the value of mm, the steeper the line. So a line with gradient 7-7 is steeper than a line with gradient 3-3.


Zero gradient

A line can have a gradient of 00. So m=0m=0. A line with a zero gradient is horizontal, for example, the line below:


Maths; Straight line graphs; KS3 Year 7; Straight line graphs

Vertical lines

How steep is a vertical line? A vertical line is 'infinitely steep', but infinity is not a number so you can't say that mm is equal to infinity. Gradient is not referred to when discussing vertical lines. 


​​

Location on the grid

The gradient tells you how steep a line is, and the yy-intercept tells you where the line sits on the coordinate grid. This is denoted by cc


The yy-intercept of a line is where the line crosses the  yy-axis. It is straightforward to read or mark the yy-intercept of a graph.  You can use the equation of a line to do this.


A vertical line will not have yy-intercept. In the special case of the vertical line being on the yy-axis, the line touching the yy-axis is everywhere. 



Example 1

What can you conclude about the gradient and the yy-intercept of the graph below?

Maths; Straight line graphs; KS3 Year 7; Straight line graphs


The line is moving upwards as it moves to the right, so its gradient is positive. It crosses the yy-axis at 1-1, so the yy-intercept is 1\underline{-1}​. 


Example 2

Consider a graph of a horizontal line that passes through the point (7,5)(7,5). What can you conclude about the line's gradient and its yy-intercept?


If a line is horizontal, it must have a zero gradient. 

Gradient = m=0\underline{m=0}​​


A horizontal line has the same yy-coordinate all the way along it. This line passes (7,5)(7,5), therefore must have yy-coordinate 55 at every point. 

yy-intercept = c=5\underline{c = 5}


The gradient and the yy-intercept are:

m=0,c=5\underline{m=0, c=5}​​


Note: Even though this example was about a graph, a diagram was not actually necessary! Sometimes you can answer graph questions without a picture.

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Exercises

FAQs - Frequently Asked Questions

Does a vertical line have a gradient?

What does it mean if a line has a gradient of zero?

What does a line with a positive gradient look like?

What is a gradient of a straight line?

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