HW 1 Solutions

HW 1 Solutions - Linear Functions Homework Solutions 1. (2...

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Linear Functions Homework Solutions 1. (2 points) Write the equation of the line which contains the points P:( - 2 , 5) and Q:(7 , 3). Give your ﬁnal answer in slope-intercept form. Using the formulas m = y 2 - y 1 x 2 - x 1 and y - y 1 = m ( x - x 1 ) we can ﬁnd the equation. Alternatively you can use y = mx + b and solve for b. m = 3 - 5 7 - ( - 2) = - 2 9 y - 5 = - 2 9 ( x - ( - 2)) y = - 2 9 ( x + 2) + 5 y = - 2 9 x - - 4 9 + 5 y = - 2 9 x + 41 9 2. (2 points) Write the equation of the line which contains the point P: (6 , - 2) and which is perpendicular to the line 5 x +2 y - 8 = 0. We again can use this formula: y - y 1 = m ( x - x 1 ). To ﬁnd m, we ﬁrst put the equation in slope-intercept form: 5 x + 2 y - 8 = 0 2 y = - 5 x + 8 y = - 5 2 x + 4 Since we want a line perpendicular, m is the negative reciprocal of the slope in this equation ( - 5 2 ). So, m = 2 5 . y - ( - 2) = 2 5 ( x - 6) y + 2 = 2 5 x - 2 5 · 6 y = 2 5 x - 12 5 - 2 y = 2 5 x - 22 5 3. (3 points) Find all real solutions to x + 20 x = 9. We want to write this as a quadratic equation. So ﬁrst, we multiple both sides by x and then we move everything to left side of the equation: x 2 + 20 = 9 x x 2 - 9 x + 20 = 0 1

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Now, you can use the quadratic formula to solve for x, or factor: x 2 - 9 x + 20 = 0 ( x - 5)( x - 4) = 0 x = 5 ,x = 4 Therefore, there are two real solutions: x=4 and x=5. 4. (3 points) Find all real solutions to 3
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HW 1 Solutions - Linear Functions Homework Solutions 1. (2...

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