Chapter 6.1 Notes
July 15, 2014 | By JulieLong |
6.1 Slope of a Line 2
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−8 −6 −4 −2 2 4 6 −4 −2 2 4 6 8 10 12 x y −4 −2 2 4 6 8 −6 −4 −2 2 4 6 8 x y Slopes of Perpendicular Lines The slopes of two oblique perpendicular lines are negative reciprocals; that is, a line with slope a , a 0, is perpendicular to a line with slope a 1 . EXAMPLE 2: Examining Slopes to Compare Lines Line PQ passes through P(-7, 2) and Q(-2, 10). Line RS passes through R(-3,-4) and S(5, 1). a) Are these two lines parallel, perpendicular, or neither? Justify the answer. b) Sketch the lines to verify the answer to part a. CYU Line ST passes through S(-2, 7) and T(2,-5). Line UV passes through U(-2, 3) and V(7, 6). a) Are these two lines parallel, perpendicular, or neither? Justify your answer. b) Sketch the lines to verify your answer to part a.
Example 1 Determining Intercepts, Domain, and Range of the Graph of a Linear Function This graph shows the fuel consumption of a scooter with a full tank of gas at the beginning of a journey. a) Write the coordinates of the points where the graph intersects the axes. Determine the vertical and horizontal intercepts. Describe what the points of intersection represent. b) What are the domain and range of this function?
We can use each representation on the previous to calculate the rate of change . The rate of change can be expressed as a fraction: The rate of change is $0.20/km; that is, for each additional 1 km driven, the rental cost increases by 20¢. The rate of change is constant for a linear relation. We can determine the rate of change from the equation that represents the linear function. Let the cost be C dollars and the distance driven be d kilometres. An equation for this linear function is: Example 1: Determining whether a Table of Values Represents a Linear Relation Which table of values represents a linear relation? Justif y the answer. a) The relation between b) The relation between temperature in degrees the current, I amps, and Celsius, C , and temperature power, P watts, in an in degrees Fahrenheit, F electrical circuit
Domain and Range Worksheet #1 Name: ____________________ State the domain and range for each graph and then tell if the grpah is a function (write yes or no). If the graph is a function, state whether it is discrete, continuous or neither. 1) Domain 2) Domain 3) Domain Range Range Range Function? Function? Function? 4) Domain 5) Domain 6) Domain Range Range Range Function? Function? Function? 7) Domain 8) Domain 9) Domain Range Range Range Function? Function? Function? 10) Domain 11) Domain 12) Domain Range Range Range Function? Function? Function?