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Linear Relationships Math Notes

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IGCSE / O Level Mathematics Notes about Linear Relationships. These notes are from Mathletics.
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   www.mathletics.com Curriculum ReadyLinear Relationships Linear Relationships  5I SERIES TOPIC 1 Linear Relatonships Mathletics Passport © 3P Learning Q   Two snails have spoed the best leuce in the garden and are travelling in straight lines towards it for dinner. Slidy Sam is following the path: 2  y x 2= -  and Slippery Shelly is following the path: 2 2  y x = - -  Which leuce are they both moving towards if it is at the point where their paths cross? G i v e  t h i s   a   g o ! Write a single sentence that describes the mathemacal meaning for these terms:You can use a small diagram/example to support your descripon. RelaonshipLinearConnuous This booklet extends on straight line concepts by invesgang the relaonship between points on a lineJoin these denions together to describe in a one sentence what you think is meant by a linear relaonship .  x -axis  y -axis   1 2 3 4 5 6 7 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0   - 1 - 2 - 3 - 4 - 5 - 6 - 7 7 6 5 4 3 2 1 A BCEIJHFDG Leuce Sam and Shelly are moving towards:  2 Linear Relatonships Mathletics Passport © 3P Learning 5I SERIESTOPIC  Linear Relationships How   does it work?     For the equaon  y x 3 4= -   Gradient-intercept form A linear relaonship is an algebraic rule that forms a connuous, straight line when graphed.Let’s review the basic linear equaon . (i) Write the gradient and  y -intercept for the graph of  y x 3 4= -  gradient m  313= =++ ^ h    y -intercept b  4= - ^ h (ii) Describe what these values mean for the graph of  y x 3 4= -  y mx b = + coecient of  x  ( m ) is the gradient the constant term ( b ) is the  y -interceptBefore graphing it is important to be able to extract the correct informaon from a linear equaon.the power of  x  and  y  is always 1 gradient-intercept form  y x 3 4= - : m  3=  graph moves 3+  vercally (slopes up) for every 1+  horizontally : b  4= -  graph passes through the point ,0 4- ^ h or the graph crosses the  y -axis at 4-   For the equaon  y x  2= +   (i) Write the gradient and  y -intercept for the graph of  y x  2= +  gradient 1 m 11= =++ ^ h    y -intercept b  2= + ^ h The 1  in front of the  x is hidden (ii) Describe what these values mean for the graph of  y x  2= + Somemes the informaon needed can appear to be ‘hidden’. : m  1=  graph moves 1+  vercally (slopes up) for every 1+  horizontally : b  2= +  graph passes through the point ,0 2 ^ h or the graph crosses the  y -axis at 2    y x  2= + Equaon is another word for rule
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