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This self-test may be taken only after you have completed all of the exercises indicated on your course-content/pacing sheet. 0600 - Self Test 6 SELF-TEST REVIEW FOR TEST 6: TWO VARIABLE LINEAR EQUATIONS, SLOPE, GRAPHS AND SQUARE ROOTS For 1 and 2 complete each ordered pair so that it is a solution to the given linear equation: 10) Find the slope of the line given by 3𝑥 − 5𝑦 = 1 1) 𝑥 − 5𝑦 = −1; ( , −2), (4, ) 11) Determine if the pair of lines is parallel, perpendicular or neither. 1 2) 𝑦 = 5 𝑥 − 2; (−10, ), ( ,1) 2 𝑦 = 𝑥−1 5 3) Complete the table of ordered pairs for the equation 2𝑥 + 𝑦 = 4 x 0 y 0 2 4) Complete the table of ordered pairs for the 1 equation 𝑦 = 2 𝑥 + 3 x 0 -4 5 𝑦=− 𝑥 2 y 0 5.) Plot the following ordered pairs: 𝐴 = (1,2), 𝐵 = (−3,0) and 𝐶 = (−2, −1) 6) Graph the equation 𝑦 = 𝑥 + 5 7) Graph the equation 𝑥 − 3𝑦 = 2 8) Find the intercepts of 2𝑥 + 3𝑦 = 6 9.) Graph the equation y=4 Find the slope of the line that passes through: 12) (−1,16) and (3,4) 13) (−2, −3) and (−2,5) 14) Use slope intercept form to graph 1 𝑦 = 2𝑥 − 2 15) Find the equation of a line where 𝑚 = −3 and 𝑏 = 2 16) Find the equation of a line passing through (−11, −12) with 𝑚 = −2. Express the equation in 𝐴𝑥 + 𝐵𝑦 = 𝐶 form. 17) Find the equation of a line passing through (7,10) and (−1, −1). Express the equation in 𝐴𝑥 + 𝐵𝑦 = 𝐶 form. 18) In 2000, crude oil field production in the USA was 2130 thousand barrels. In 2007 US crude oil production dropped to 1850 thousand barrels. a) Write two ordered pairs of the form (years after 2000, crude oil production). b) Assume the relationship between years after 2000 and crude oil production is linear over this period. Use the ordered pairs from part (a) to write an equation of the line relating years after 2000 to crude oil production. c) Use the linear equation from part (b) to estimate crude oil production in the US in 2010, if this trend were to continue. 19) Find √16 27) Find the equation of a line passing through (-4,3) and (-4, 5). 28) Find the slope of a line which passes through the points (5,3) and (19,3) 29) Find the slope of a line which passes through the points (2,1) and (2,-5) 30) Find the slope of a line which is 2 perpendicular to 𝑦 = 3 𝑥 + 2 31) Find the slope of a line which is parallel to a line a passing through the points (6,-1) and (-4,-10). 32) A car traveling along a road rises by 16 feet for every 100 feet of horizontal motion. Find the grade of the road. 33) When walking up a set of stairs one makes a vertical motion of 16ft and a horizontal motion of 8 ft. Find the slope of the stairs. 1 20) Find √121 21) Find −√169 22) Find √−36 23) Use the Pythagorean theorem to find x: 7 X 24 24) Simplify: √9 + 16 25) Evaluate √𝑃𝐴 If A=5 and P=20 26) Find the equation of a line passing through (0,2) and (3,2) 34) Verify that the points (2,1), (0,0) and (−2, −1) are all on the same line. Do this by computing the slope between each combination of points and verify that it is always the same. 35) A student borrows $12,000 from her parents to buy a car. She plans to pay them back at the rate of $300 per month. a.) Write a linear equation to represent the amount she owes after she makes x payments. b.) How many months will it take to pay off the loan? Answers: 1) (−11, −2), (4,1) 2) (−10, −4), (15,1) 3) x y 0 4 2 0 1 2 8) (0,2), (3,0) 9) 4) X 0 -4 -6 y 3 1 0 3 10) 𝑚 = 5 11) Perpendicular 12) 𝑚 = −3 13) Undefined slope 14) 5) y .A x .B .C 6) 7) 15) 𝑦 = −3𝑥 + 2 16) 2𝑥 + 𝑦 = −34 17) 11𝑥 − 8𝑦 = −3 18) a) (0,2130), (7,1850) b) 𝑦 = −40𝑥 + 2130 c) 1730 thousand barrels 19) 4 20) 1/11 21) -13 22) not a real number 23) X=25 24) 5 25) 10 26) Horizontal line 𝑦 = 2 27) Vertical line 𝑥 = −4 28) Slope is 0 29) Slope is undefined 30) Slope is -3/2 31) Slope is 9/10 32) 16% 33) Slope is 2 34) Slope is always ½ 35) a) 𝑦 = −300𝑥 + 12000 b) 40 months 0600 Self Test6 Created for fall 2014