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Created page with "==Key Stage 4== ===Meaning=== When a relationship between two variables is '''linear''' they increase by a constant amount in relation to one another. ===About Proportion..."
==Key Stage 4==
===Meaning===
When a relationship between two [[variable]]s is '''linear''' they increase by a constant amount in relation to one another.
===About Proportional Graphs===
: A [[Scatter Graph|scatter graph]] showing a '''linear''' relationship has straight [[Line of Best Fit|line of best fit]].
: On a [[proportional]] [[Scatter Graph|scatter graph]] when one [[variable]] increases, the other increase or when one increases the other decreases.
: A [[proportional]] graph may have a non-zero [[y-intercept]].
: If the [[Line of Best Fit|line of best fit]] has a [[y-intercept]] of zero then it is called '[[Directly Proportional|directly '''proportional''']]'.
===Examples===
{| class="wikitable"
|-
|[[File:ProportionalSketchGraph1.png|center|200px]]
|[[File:ProportionalSketchGraph2.png|center|200px]]
|[[File:DirectlyProportionalSketchGraph.png|center|200px]]
|-
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[proportional]] where x increases, y increases.
<math>y = mx + c</math>
Where m, the [[gradient]], is positive.
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[proportional]] where x increases, y decreases.
<math>y = mx + c</math>
Where m, the [[gradient]], is negative.
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[Directly Proportional|directly proportional]] where x doubles, y doubles.
<math>y = mx</math>
Where m, the [[gradient]], is positive.
|}
===Meaning===
When a relationship between two [[variable]]s is '''linear''' they increase by a constant amount in relation to one another.
===About Proportional Graphs===
: A [[Scatter Graph|scatter graph]] showing a '''linear''' relationship has straight [[Line of Best Fit|line of best fit]].
: On a [[proportional]] [[Scatter Graph|scatter graph]] when one [[variable]] increases, the other increase or when one increases the other decreases.
: A [[proportional]] graph may have a non-zero [[y-intercept]].
: If the [[Line of Best Fit|line of best fit]] has a [[y-intercept]] of zero then it is called '[[Directly Proportional|directly '''proportional''']]'.
===Examples===
{| class="wikitable"
|-
|[[File:ProportionalSketchGraph1.png|center|200px]]
|[[File:ProportionalSketchGraph2.png|center|200px]]
|[[File:DirectlyProportionalSketchGraph.png|center|200px]]
|-
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[proportional]] where x increases, y increases.
<math>y = mx + c</math>
Where m, the [[gradient]], is positive.
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[proportional]] where x increases, y decreases.
<math>y = mx + c</math>
Where m, the [[gradient]], is negative.
| style="height:20px; width:200px; text-align:center;" |This [[Scatter Graph|scatter graph]] shows a [[linear]] relationship that is [[Directly Proportional|directly proportional]] where x doubles, y doubles.
<math>y = mx</math>
Where m, the [[gradient]], is positive.
|}