Miss Hudson’s Maths

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

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

y= 2 x + 3 Miss Hudson’s Maths

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

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

Changing the Rule Again  What happens if we change the again slight again??  Our new rule is y = -2 x - 3 xy 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= Miss Hudson’s Maths

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

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

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

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

 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

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

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

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

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