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Math 1090 Quiz 1 Solution January 26th, 2015 Answer the following 4 questions in the space provided. The value of every question is indicated at the beginning. Time: 10 minutes. Name: UID: 1. (5 points) Find the slope and the y-intercept of the line 2x + 7y = 3. Solution. The point here is to solve for y, namely to obtain an expression of the form y = mx + b. Then m will be your slope, and (0, b) will be your y-intercept. In this case we have 2x + 7y = 3 7y = −2x + 3 2 3 y =− x+ 7 7 So the slope is m = − 27 and the y-intercept is the point 0, 73 . 2. (5 points) Find the equation of the line that passes through the point (−3, 8) and is perpendicular to the line from question 1. Solution. Remember that two lines are perpendicular if their slopes m1 and m2 satisfy the relation m2 = − m11 . Since the line from question 1 has slope m1 = − 27 , a line perpendicular to it must have slope m2 = − m11 = − −12 = 72 . 7 We thus need to find the equation of a line with slope 27 that passes through the point (−3, 8). Using the point-slope formula, the equation will be 7 y − 8 = (x − (−3)) 2 7 y − 8 = (x + 3) 2 3. (5 points) Is the line that goes through the points (−3, 8) and (4, 6) parallel to the line from question 1? Solution. Remember that 2 lines are parallel if they have the same slope. The slope of the line from question 1 was m = − 27 . The slope of the line that goes through two points (x1 , y1 ) and (x2 , y2 ) is given by y2 − y1 m= x2 − x1 so for the points (−3, 8) and (4, 6) we have m= 6−8 2 =− 4 − (−3) 7 Since both slopes coincide, the 2 lines are parallel. 4. (5 points) Find 3 consecutive integers whose sum is 36. Solution. We can write three consecutive integers as a, a + 1 and a + 2, where a is some integer. We need to find an integer a such that a + (a + 1) + (a + 2) = 36 3a + 3 = 36 3a = 33 a = 11 so a = 11 is your solution. Page 2