1 Lesson 13, Section 2.4 A Slopes and Graphs of Vertical or Horizontal Lines 1. Slope of a horizontal line ),(1yx ),(2yx #012=−−=xxyym Zero divided by any number is zero. The slope of a horizontal line is zero. 2. Graph of a horizontal line Graph 4)(−==yxf x y -4 -4 -4 -4 If a line is of the form, byxf==)(, then the line is horizontal with a y-intercept at (0, b) and the slope of this line is zero. 3. Slope of a vertical line 0#12=−−=xxyym A fraction with a 0 denominator is undefined. The slope of a vertical line is undefined. ),(1yx ),(2yx2 4. Graph of a vertical line Graph x + 2 = 4 x 2 2 2 y If a line is of the form, ax=, then the line is vertical with an x-intercept at (a, 0) and the slope of this line is undefined. Find the slope and graph of each. Ex 1 1043=+x Ex 2 32−=y3 B Intercepts An ordered pair (0, b) is the y-intercept of a line and an ordered pair (a, 0) is the x-intercept of a line. Notice: One of the coordinates is zero. Lines are easily graphed using the intercepts. Find the intercepts and graph. Ex 3 141−= xy Ex 5 23)(+=xxf Ex 4 1834=+yx4 C Applications Many real life situations can be represented as a linear function (usually a function of time). The initial amount or number is the b and the rate of change is the m. Ex 6 Molly Jones agrees to pay $8000 down payment plus $350 a month to pay for a car. a) Write a linear function to illustrate her total payments as a function of the number of months. Use this function to answers parts (b) and (c). b) How much has Molly paid on the car in 5 months from purchase? c) If the total (including any interest or fees) that Molly needs to pay is $20,600, how many months will it take to pay off the car? Ex 7 One plan from Jitterbug Phones charges a customer $140 for a phone and fees to open an account plus payments of $30 a month (for 30 minutes per month). a) Write a cost function to represent the total paid for this plan from the beginning. Use your function to find or predict the following. b) How much has a customer with this plan paid in 9 months? c) How long will it take before the customer has paid $1640?5 A Linear Function is one of the form bmxy+=. Notice that the x and y are only 1st powers. A Linear Equation in Standard form is the form Ax By C+ =, where A > 0 and A, B, and C are integers. Any other type of function is called a non-linear function. Ex 8 Identify each equation or function as linear or non-linear. a) 943=+yx b) 43)(−=ttg c) 32)( −= xxf d) xxy 23−= e) 105=y f) 2)( −=
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