2. Straight Line Graphs

3. 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

4. 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!

5. 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.

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

7. Identifying gradient & y intercept from equation y = 2x + 2 y = 5x – 9 y = -2x + 1 y = 1/2x -3 y = -x + 10 2y = 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

8. 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 ÷ 1 = 2 Finding m and c from graphs y = 2x +3y = mx +c

9. 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

10. 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)

11. 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 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 = 4 2 1 2 Gradient = 4 ÷2 = 2 y intercept = -3 2 6 Gradient = 6 ÷2 = 3 y intercept = 2 2 1 Gradient = 2 ÷1 = -2 y intercept = 6 4 3 Gradient = 3 ÷3 = 1 y intercept = 3 3 Gradient = 0 y intercept = 4 2 2 Gradient = 2 ÷2 = -1 y intercept = 2 Gradient = 0 x intercept = 2

12. 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