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

Starter: What are the co-ordinates? 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 -3 -4 -5 -6 (-4, -2) (4, 6) (-1, 1) (6, 5) (4, -2) (5, 3) (2, -3) (3, 2) (7, 1) (-2, -4) (1, 5) (-7, 2) (-4, 3) (-2, -1) Skip Starter

All straight lines can be written in the form y = mx + c Knowledge: All straight lines can be written in the form y = mx + c 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!

c is the constant value – this part of the function does not change. 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”.

y x Finding m and c Look at the straight line. 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 -3 -4 -5 -6 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. y = mx +c y = 2x +3 So m = 2

y x Another example We can see that c = -2 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 -3 -4 -5 -6 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… vertical change by the… horizontal change. The gradient, m = 2/4 = ½ 2 y = ½x - 2 y = mx +c 4

Plenary: Assessing ourselves 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 -3 -4 -5 -6 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

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