1 / 11

Linear Functions

Linear Functions . Chapter1, Section3. Linear Functions. A linear function is a function that can be written in the form where a and b are constants. Notice that the exponent on the variable is a 1, hence first degree (linear).

ghazi
Télécharger la présentation

Linear Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear Functions Chapter1, Section3

  2. Linear Functions • A linear function is a function that can be written in the form where a and b are constants. Notice that the exponent on the variable is a 1, hence first degree (linear). EX: Which of the following equations are linear functions?

  3. Intercepts The points where the graph crosses or touches the x-axis and the y-axis are called the x-intercept and the y-intercept, respectively. Graphically these points can be seen on the axes. To find the y-intercept algebraically, set x = 0 and solve the equation for y. If the solution is b, then the point on the graph is (0, b). To find the x-intercept algebraically, set y = 0 and solve for x. If a is the solution, then the resulting point is (a, 0).

  4. Example 1 A business property is purchased with a promise to pay off a $60,000 loan plus $16,500 interest on this loan by making 60 monthly payments of $1275. The amount of money, y remaining to be paid on $76,500 is reduced by $1275 each month. This can be modeled the linear function: y = 76,500 – 1275x. Find the intercepts of this equation. Interpret the intercepts for this model. What limits should there be? Use the intercept to sketch the graph. Example 2 Find the x and y-intercepts for the equation, . What does the graph look like?

  5. Slope of a Line The slope of a line is defined as: To calculate the value of the slope, we use the formula as follows. When two points are given,

  6. Find the slope of the line through the points (-3,2) and (5,-4). What does the slope mean? Find the slope of the line joining the x and y-intercept points in the previous Example 2. Example 3

  7. The Relationship Between Orientation of a Line and its Slope m>0 m=0 m<0 m is undefined

  8. Using Example 2, y = 76,500 – 1275x. • What is the slope and y-intercept? • How does the amount owed on the loan change as the number of months increases? Example 4 Slope and y-intercept The slope of the graph of the equation y = mx + b is m and the y-intercept is b, or the point on the graph (0,b). From this form we get our linear function: f(x) = mx + b.

  9. Use the graph of the function y = 16.908x – 20.945 where x is the number of years after 1990 and y is the sales in billions of dollars. • What is the slope of the graph of the function? • What is the rate at which the sales grew during this period? Example 5 Constant Rate of Change The rate of change of the linear function y = mx + b is the constant m, the slope of the graph of the function. 200 180 160 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Years after 1990

  10. Revenue, Cost and Profit • Revenue is the money from sales of goods or services. • Cost is the expense generated in producing those good or services. • Profit is the difference between Revenue and Cost. Its what is left over from the production and sale of goods and/or services: P(x) = R(x) – C(x) When these functions are linear the rates of change are called MARGINAL COST, MARGINAL REVENUE, AND MARGINAL PROFIT. (It’s the slopes of the functions.)

  11. Example:Marginal Revenue and Marginal Profit • A company produces and sells a product with revenue given by R(x) = 89.50x dollars per unit x and cost given by C(x) = 54.36x + 6790 dollars per unit x. • What is the marginal revenue for this product and what does it mean? • Find the profit function. • What is the marginal profit for this product and what does it mean?

More Related