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Published byBeatrice Cordill Modified over 2 years ago

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Objective Understand that all straight line graphs can be represented in the form y=mx+c, and be able to state the equation of given graphs

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All straight lines can be written in the form y = mx + c Knowledge: You need to be able to write down the equation of a straight line by working out the values for m and c. It’s not as hard as you might think!

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y = mx + c m is the gradient of the line Why use m? This type of equation was made popular by the French Mathematician Rene Descartes. “m” could stand for “Monter” – the French word meaning “to climb”. c is the constant value – this part of the function does not change.

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y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 Look at the straight line. It is very easy to find the value of c – this is the point at which the line crosses the y-axis So c = 3 Finding m is also easy in this case. The gradient means the rate at which the line is climbing. Each time the lines moves 1 place to the right, it climbs up by 2 places. So m = 2 Finding m and c y = 2x +3y = mx +c

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y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 We can see that c = -2 Another example As the line travels across 1 position, it is not clear how far up it has moved. But… Any right angled triangle will give use the gradient! Let’s draw a larger one. In general, to find the gradient of a straight line, we divide the… 2 4 vertical change by the… horizontal change. The gradient, m = 2 / 4 = ½ y = mx +cy = ½x - 2

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y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 Plenary: Assessing ourselves y = 2x + 4 y = 2x - 3 y = 3x + 2 y = -2x + 6 y = x + 3 y = 4 y = 4x + 2 y = -x + 2 x = 2

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Did you meet the objective? Understand that all straight line graphs can be represented in the form y=mx+c, and be able to state the equation of given graphs

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