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Test 2 MAT 1111 Summer 2011 Name______________________________ Simplify all answers and show your work! 1) In the linear equation 2x + 7y = 14, what is the x-intercept? __(7, 0)___ y-intercept? __(0, 2)__ 2) Lines that are parallel have the same __slope__. 3) In order to find the equation of a line, we must have a _slope_ and a __point___. 4) When translating phrases into mathematical expressions (like in # 9), “of” means to _multiply_ and “per” means to _divide__. 5) Find the equation of the line having the following properties. 5 6 a) m = , passing through (4, –3) b) m = − , passing through (0, –2) 3 13 5x – 3y = 29 or y= 5 29 x− 3 3 y= − c) Parallel to 8x + 3y = –15 and passing through (6, –2) 8x + 3y = 42 or 6 x–2 13 or 6x + 13y = –26 d) Passing through (–4, –1) and (1, –9) 8 y = − x + 14 3 8x + 5y = –37 or 8 37 y= − x− 5 5 6) If f(x) = –x + 21 and g(x) = 2x + 3 , find the following: a) f(–10) b) f(2x + 4) 31 –2x + 17 c) g(0) d) g(6) 3 15 7) Find the domain of each of the following functions: a) f ( x ) = x + 4 b) f(x) = 18x2 – 3 x ≥ –4 all real numbers 8) Translate each phrase into a mathematical expression: a) Eleven less than a number b) Three more than twice a number x – 11 2x + 3 c) f ( x ) = 4x x −9 all real numbers except 9 9) Solve the system of equations: 3x − 4 y = −17 5x + y = −13 (–3, 2) 10) Solve for x: 7 x 2x − 7 5 − = 18 6 9 x = –11 11) Graph the equation of the line: 3x + 2y = –12 See graph below 12) Graph the line: f(x) = 5 x−2 3 See graph below 13) A shopkeeper orders a total of 60 pounds of almonds and cashews for a total of $162. If almonds cost $3 a pound and cashews cost $2 a pound, how many almonds did the shopkeeper order? 42 pounds worth of almonds