Quiz 11A sol - Solutions to Quiz 11A www.math.ufl.edu/˜harringt 1 Let x = 5 be the line L(a Find the slope of a line that is parallel to L m =

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Unformatted text preview: Solutions to Quiz 11A www.math.ufl.edu/˜harringt October 27, 2007 1. Let x = 5 be the line L. (a) Find the slope of a line that is parallel to L. m = undefined (b) Find the slope of a line that is perpendicular to L. m = 0 Note: To see why, please graph x = 5. 2. Find the equation for the line containg the x-intercept 2 and the yintercept 3. Write your answer in slope-intercept form. METHOD 1: With x-intercept 2 and y-intercept 3, we know that the line contains the points (0, 3) and (2, 0). Now we can find the slope. m= ∆y 3 3 = =− ∆x −2 2 Hence, y = −3 x + b. Since we already know that the y-intercept is 3, 2 then, b = 3. So, y = −3 x + 3. 2 METHOD 2: The studious student could recall from the homework on page 193 number 82 that xy + =1 ab 1 where a is the nonzero x-intercept and b is the nonzero y-intercept. Thus, we have the following: xy + =1 23 y x = − +1 3 2 2 y = − x+3 3 3. Determine the validity of each statement. (a) ”Every line has two distinct intercepts.” This statement is FALSE. Consider the line y = 3. This line only has one intercept namely, the y-intercept (0, 3). (b) ”Perpendicular lines have slopes that are reciprocals of one another.” This statement is FALSE. The correct statement should read ”Perpendicular lines have slopes that are NEGATIVE reciprocals of one another.” (c) ”A system of equations containing two variables always has a least one solution.” This statement is FALSE. Consider the following system: y =x+3 y =x+5 This system has no solution. (Why?) So a system of two variables does not always have at least one solution. 2 ...
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This note was uploaded on 07/12/2011 for the course MAC 1140 taught by Professor Williamson during the Fall '08 term at University of Florida.

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Quiz 11A sol - Solutions to Quiz 11A www.math.ufl.edu/˜harringt 1 Let x = 5 be the line L(a Find the slope of a line that is parallel to L m =

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