Presentation on theme: "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."— Presentation transcript:
1ObjectiveUnderstand that all straight line graphs can be represented in the form y=mx+c, and be able to state the equation of given graphs
2All straight lines can be written in the form y = mx + c Knowledge:All straight lines can be written in the form y = mx + cYou 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!
3c is the constant value – this part of the function does not change. y = mx + cm is the gradient of the lineWhy 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”.
4y x Finding m and c Look at the straight line. 12345678–7 –6 –5 –4 –3 –2 –1-1-2-3-4-5-6It is very easy to find the value of c – this is the point at which the line crosses the y-axisSo c = 3Finding 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 +cy = 2x +3So m = 2
5y x Another example We can see that c = -2 12345678–7 –6 –5 –4 –3 –2 –1-1-2-3-4-5-6As 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 = ½2y = ½x - 2y = mx +c4