CHAPTER 1 LESSON 3 Linear Functions

WHAT IS A LINEAR FUNCTION?  A linear function is a function that can be written in the form f(x)= ax+b where a and b are constants.

WHAT IS NOT A LINEAR FUNCTION?  Anything with a variable raised to a power other than 1  Anything with a variable in the denominator  Anything with two variables multiplied together

FINDING Y-INTERCEPTS  To find the y-intercept of a linear equation, set x value equal to zero and solve for y.

FINDING X-INTERCEPTS  To find x-intercepts, set y value equal to zero and solve for x.

FINDING INTERCEPTS GRAPHICALLY  Graph the function on your calculator  To find y-intercept  Press 2 nd button, then TRACE button  Select option 1:value  Input value of 0 for x  Press ENTER  Y-value given is y-intercept  To find x-intercept  Press 2 nd button, then TRACE button  Select option 2: zero  Select Left and Right Bounds for zero  Press ENTER  X-value given is x-intercept

EXAMPLE  A business property is purchased with a promise to pay off $60,000 loan plus the $16,500 interest on this loan by making 60 monthly payment of $1,275. The amount of money, y, remaining to be paid on $76,500 (the loan plus interest) is reduced by $1,275 each month. Although the amount of money remaining to be paid changes every month, it can be modeled by the linear function y= x, where x is the number of monthly payments made. We recognize that only integer values of x from 0 to 60 apply to this application.  A) Find the X and Y intercept of the graph of this function  B) Interpret the intercepts in the context of this problem situation.  C) How should X and Y be limited in this model so that they make sense in the application?  D) Use the intercepts and Results of part c to sketch the graph of the given equation

SLOPE OF A LINE

RELATION BETWEEN ORIENTATION OF LINE AND ITS SLOPE  If a line is going up from left to right, it has a positive slope.  If a line is going down from left to right, it has a negative slope.  Horizontal lines have a slope of 0.  Vertical lines have an undefined slope.

SLOPE INTERCEPT FORM  y= mx + b  m is the slope of the line, also known as the rate of change  b is the y-intercept

SPECIAL FUNCTIONS  Given slope intercept form y= mx + b  Constant Function  m = 0, graph looks like a horizontal line  Identity Function  m = 1 and b = 0

HOMEWORK  Pages  1,3,4,7,9,13-15,17,20, 21,27,29,30, 35,37- 39,43,47,49,51,52,57,59,61,62