1. Miss Hudson’s Maths

2. Graphing  When we see the rule y = 2 x + 3 we know that a line can be drawn using it.  But what if we are not given a table with our coordinates for our points??  What we can do is substitute values into out rule to give us those points. Miss Hudson’s Maths

3. Substitution xy 1 2 3 4 We can now draw our line y = 2 x + 3 y = 2 x 1 + 3 y = 5 y = 2 x + 3 y = 2 x 2 + 3 y = 7 y = 2 x + 3 y = 2 x 3 + 3 y = 9 y = 2 x + 3 y = 2 x 4 + 3 y = 11 5 7 9 11 Miss Hudson’s Maths

4. y= 2 x + 3 Miss Hudson’s Maths

5. Changing the Rule  What happens when we change the rule slightly??  The new rule is y = 2 x - 3 xy 1 2 3 4 y = 2 x – 3 y = 2 x 1 – 3 y= -1 y = 2 x – 3 y = 2 x 3 – 3 y= 3 y = 2 x – 3 y = 2 x 4 – 3 y= 5 y = 2 x – 3 y = 2 x 2 – 3 y= 1 1 3 5 Miss Hudson’s Maths

6. y= 2 x + 3 y= 2 x - 3 Miss Hudson’s Maths

7. Changing the Rule Again  What happens if we change the again slight again??  Our new rule is y = -2 x - 3 xy 1 2 3 4 y = -2 x – 3 y = -2 x 1 – 3 y= -5 y = -2 x – 3 y = -2 x 4 – 3 y= -11 y = -2 x – 3 y = -2 x 3 – 3 y= -9 y = -2 x – 3 y = -2 x 2 – 3 y= -7 -5 -7 -9 -11 Miss Hudson’s Maths

8. y= 2 x + 3 y= 2 x - 3 y=- 2 x - 3 Miss Hudson’s Maths

9. Changing the Rule Again  What happens when we change the rule again slightly??  The new rule is y = -2 x + 3 xy 1 2 3 4 y = -2 x + 3 y = -2 x 1 + 3 y= 1 y = -2 x + 3 y = -2 x 3 + 3 y= -3 y = -2 x + 3 y = -2 x 4 + 3 y= -5 y = -2 x + 3 y = -2 x 2 + 3 y= -1 1 -3 -5 Miss Hudson’s Maths

10. y= 2 x + 3 y= 2 x - 3 y= - 2 x - 3 y= - 2 x + 3 What do you notice? Miss Hudson’s Maths

11. The Rule  We know that the general rule is: y = m x + c Where m is the constant difference And c is the starting number or when x=0  There is a much simpler way to draw the line without substituting values into the rule. Miss Hudson’s Maths

12.  Another way we can define this rule is: m is the slope of the line and c is the y intercept  The slope of the line is called the gradient  The y intercept is where the line cuts the y axis Miss Hudson’s Maths

13. Gradient or the slope  When we look at the gradient or the slope of a line we write it in the form of: rise run This will make more sense when we look at a graph. Miss Hudson’s Maths

14. y= 2 x + 3 +2 +1 Gradient: m= 2 1 y-intercept c = 3 y= 2 x + 3 Miss Hudson’s Maths

15. Gradient (m)= 1 1 y-intercept c = -1 y= 1 x - 1 Miss Hudson’s Maths

16. We are given the rule: y= 3 x + 1 c = 1 m = 3 1 Miss Hudson’s Maths