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MAT 150 – Algebra Class #3. Today’s Topics: Identify Linear Functions Intercepts/Slopes Graph Linear Functions Rate of Change Identity and Constant Functions Apply Linear Revenue, Cost, and Profit. Linear Functions . A function whose graph is a line is a linear functions .
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MAT 150 – Algebra Class #3 Today’s Topics: Identify Linear Functions Intercepts/Slopes Graph Linear Functions Rate of Change Identity and Constant Functions Apply Linear Revenue, Cost, and Profit
Linear Functions • A function whose graph is a line is a linear functions. Linear Function A linear function is a function that can be written in the form , where a and b are constants. Ex) Linear: Non-Linear: y= -17.8x – 6 y = 4
Intercepts Intercepts are points that cross the x-axis and the y-axis. To Find the y-intercept: Let x = 0 and solve for y To Find the x-intercept: Let y = 0 and solve for x Example: Find the x-intercept and y-intercept of the graph 4x-12y =22
Loan Balance A student promised to pay off a $35,000 loan plus the $7,000 interest on this loan by making 120 monthly payments of $350. Although the amount of money remaining to be paid changes every month, it can be modeled by the linear functions where x is the number of monthly payments made. • Find the x-intercepts and the y-intercepts of the graph of this liner equation. • Interpret the intercepts in the context of this problem situation. • How should x and y be limited in this model so that they make sense in the application? • Use the intercepts and the results of part (c) to sketch the graph of the given equation.
Finding Slope Given 2 Points Find the slope of each: • (-3, 2) and (5, -4) • (8, -3) and (7, -4)
Part I - Slope Match each equation with the possible slope: y = 2x + 3 y = 5 x = 2 y = - 2x + 5
Slope and y-Intercept of a Line The slope of the graph of the equation is m and the y-intercept of the graph b, so the graph crosses the y-axis at (0,b).
Special Linear Functions Constance Function Identity Function y = b, where b is a real number y = x
Revenue, Cost and Profit The profit that a company makes on its product is the difference between the amount received from sales (revenue) and the production and sales cost. Goes a little something like this in the math world: Where, P(x) = profit from sale of x units R(x) = total revenue from sale of x units C(x) = total cost of production and sale of x units
iWow Apple manufactures a 16GB Wi-Fi-only iPad 3 and sells them for $499. The cost incurred in the production and sale of the iPad are $500,000* plus $316** for each iPad produced and sold. Write the profit function for the production and sale of x iPads. *Yeah….I made this up. Judge me! ** According to http://www.ijailbreak.com/ipad/how-much-does-new-ipad-cost-to-make
Assignment Pg. 54-57 #1-19 odd #35-38 all #42-43