Straight Line Graphs

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. State the gradient and y intercept given the equation

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!

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 equation does not change.

Identifying gradient & y intercept from equation y = 3x + 5 Gradient = 3 y intercept = 5

Identifying gradient & y intercept from equation y = 2x + 2 y = 5x – 9 y = -2x + 1 y = 1/2x -3 y = -x y = 4x + 3 m = 2, c = 2 m = 5, c = -9 m = -2, c = 1 m = 1/2, c = -3 m = -1, c = 10 m = 2, c = 1.5

y x – 7 – 6 – 5 – 4 – 3 – 2 – 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 ÷ 1 = 2 Finding m and c from graphs y = 2x +3y = mx +c

y x – 7 – 6 – 5 – 4 – 3 – 2 – 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

Positive or negative gradient? Consider the straight lines shown below: (a) (c) (b) (d) (e) Can you split the lines into two groups based on their gradients ? Lines (a) (c) and (d) slope upwards from left to right. Lines (b) and (e) slope downwards from left to right. Positive gradient Negative gradient (a) (c) (d) (b) (e)

y x – 7 – 6 – 5 – 4 – 3 – 2 – Assessing ourselves y = 2x + 4 y = 2x - 3 y = 3x + 2 y = -2x + 6 y = x + 3 y = 4 y = -x + 2 x = 2 Gradient = 2 ÷1 = 2 y intercept = Gradient = 4 ÷2 = 2 y intercept = Gradient = 6 ÷2 = 3 y intercept = Gradient = 2 ÷1 = -2 y intercept = Gradient = 3 ÷3 = 1 y intercept = 3 3 Gradient = 0 y intercept = Gradient = 2 ÷2 = -1 y intercept = 2 Gradient = 0 x intercept = 2

Did you meet the objective? You should : Be able to state the equation of graphs in the form of y = mx + c Be able to state the gradient & y intercept from any given equation