Objective Understand that all straight line graphs can

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 (-4, -2)1) (4, (-1, 6) (6, (5, (4, 5)3) -2) (2, -3) (3, (7, 2)1) (-2, -4)2) (1, (-7, 5) (-4, 3)-1) (-2, 8 7 6 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 1 2 3 4 5 6 7 8 x -2 -3 -4 -5 -6 Skip Starter

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”.

Finding m and c Look at the straight line. y 6 It is very easy to find the value of c – this is the point at which the line crosses the y -axis 5 So c = 3 8 7 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 1 2 3 4 5 -2 -3 -4 -5 -6 yy == mx 2 x +3 +c 6 7 8 x 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

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

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