chapter1ProblemsAndSolutions

# - Chapter 1 Review of Straight Lines 1.1 Find the slope and y intercept of the following straight lines(a y = 4 x 5(b 3 x 4 y = 8(c 2 x = 3 y(d y

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Unformatted text preview: Chapter 1 Review of Straight Lines 1.1 Find the slope and y intercept of the following straight lines: (a) y = 4 x- 5 (b) 3 x- 4 y = 8 (c) 2 x = 3 y (d) y = 3 (e) 5 x- 2 y = 23 Detailed Solution: (a) This is the slope-intercept equation for the line. The slope is 4 and the y intercept is- 5. (b) Solving the equation for y yields y = 3 4 x- 2. The slope is 3 4 and the y intercept is- 2. (c) Solving the equation for y gives y = 2 3 x = 2 3 + 0. The slope is 2 3 and the y intercept is 0. (d) y = 3 can be written as y = 0 · x + 3. The slope is 0 and the y intercept is 3. (e) Solving the equation for y yields y = 5 2 x- 23 2 . The slope is 5 2 and the y intercept is- 23 2 . 1.2 Find the equations of the following straight lines (a) Through the points (2,0) and (1,5). (b) Through (3,-1) with slope 1/2. (c) Through (-10,2) with y intercept 10. (d) The straight line shown in Figure 1.1. v.2005.1 - September 4, 2009 1 Math 102 Problems Chapter 1 1 y = -8 + 18 x - 9 x 2 Figure 1.1: Figure for problem 1.2(d) Detailed Solution: (a) y- x- 2 = 5- 1- 2 =- 5 so y =- 5( x- 2) =- 5 x + 10. (b) y + 1 x- 3 = 1 2 leads to y = 1 2 x- 5 2 . (c) y- 10 x = 2- 10- 10 = 4 5 . After simplifying we get y = 4 5 x + 10. (d) The quadratic shown has roots r 1 , 2 = (- 18 ± √ 18 2- 4 · 8 · 9) / 2(- 9) = 2 / 3 , 4 / 3 , The line goes through the larger of these roots, (4 / 3 , 0), and its y-intercept is (0 , 1), as can be seen on the graph. Therefore, the slope is m =- 1 / (4 / 3) =- 3 / 4. The equation is then y =- (3 / 4) x + 1. 1.3 Find the equations of the following straight lines: (a) Slope- 4 and y intercept 3. (b) Slope 3 and x intercept- 2 / 3. (c) Through the points (2 ,- 7) and (- 1 , 11). v.2005.1 - September 4, 2009 2 Math 102 Problems Chapter 1 (d) Through the point (1 , 3) and the origin. (e) Through the intersection of the lines 3 x + 2 y = 19 and y =- 4 x + 7 and through the point (2 ,- 7). (f) Through the origin and parallel to the line 2 x + 8 y = 3. (g) Through the point (- 2 , 5) and perpendicular to the line y =- 1 2 x + 6. Detailed Solution: (a) The slope-intercept equation for a straight line is y = mx + b where m is the slope and b is the y intercept for the line, so the equation is y =- 4 x + 3. (b) Since the slope of the line is 3, its slope-intercept equation has the form y = 3 x + b . To find the value of b , note that the line passes through the point (- 2 / 3 , 0) ( x intercept). Substituting x =- 2 / 3, y = 0 into the equation gives: 0 = 3 parenleftbigg- 2 3 parenrightbigg + b Solve for b 0 =- 2 + b b = 2 So the equation of the line is y = 3 x + 2. (c) The slope of the line is 11- (- 7)- 1- 2 =- 6 Using the point-slope equation with the point (2 ,- 7) yields: y- (- 7) x- 2 =- 6 y + 7 =- 6( x- 2) y =- 6 x + 12- 7 y =- 6 x + 5 (d) The line passes through (0 , 0) and (1 , 3). The slope of the line is 3- 1- = 3 The y intercept is 0 since the line passes through the origin. Therefore, the equation of the line is y = 3 x ....
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## This note was uploaded on 05/19/2011 for the course MATH 102 Math 102 taught by Professor Allard during the Winter '09 term at The University of British Columbia.

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- Chapter 1 Review of Straight Lines 1.1 Find the slope and y intercept of the following straight lines(a y = 4 x 5(b 3 x 4 y = 8(c 2 x = 3 y(d y

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