Linear functions

2. Linear functions The equation of a line can be written in the form: y = where m = and b = Recall that the y-value is called the dependent variable as it depends upon the x-value. The x-value is called the independent variable as it can take on any value we wish and then the y-value is calculated. mx + b gradient y-intercept This is called a linear function because when it is graphed it forms a straight line.

3. Other functions We will look at several other types of functions. Quadratics: y = the highest power is Cubic y = the highest power is Exponential y = the x is in the Hyperbolic y = ax2+ bx + c squared. ax3+ bx2 + cx + d cubed. ax power. a/x or xy = a

4. 1 2 5 3 6 15 Finding the equation from a table of values Sometimes we are given a table of values and asked to find the equation of the line that it forms. To find the equation of a linear function such as this, we first work out the gradient, then the y-intercept. To find the gradient we need to know the rise and the run or change in y-values or change in x-values. 5 = 3 × 1 + b so b =  y = 3x + 2 If y = mx + b Then y = Sub in ANY point to find b. 3x + b 2

5. Example 1 Sian sells used cars and is paid $200 per week plus 5% commission on her sales. • Form an equation for her pay • Complete the table of values. • Graph the results. • From the graph: • i) if Sian sells $16 000 what is her pay? • ii) if Sian is paid $700, how much did she sell? a) P = 0·05S + 200 200 400 800 1200 d i) d ii) $1000 $10 000

6. Example 2 State what type of function (linear, quadratic, cubic, exponential or hyperbolic) each of the following are. a) y = 8  5x b) y = x3 c) xy = 7 d) y = 3x e) y = x2 +7 f) y = 5/x g) y = 10  5x + x2 h) x + y = 8 i) y = x3 + x2 7x + 9 j) k) l) Linear Cubic Hyperbolic Exponential Quadratic Hyperbolic Quadratic Linear Cubic Quadratic Hyperbolic Exponential

7. Today’s work Exercise 12A pg 361 2efgh, 3, 5, 9, 10