Find the equation ofthe line through the given point that is perpendicular to the given line (The slope of the perpendicular line is the negative reciprocal ofthe slope of the given line if ti vertical nor horizontal.) 2 (a) y: -X+9. R(8.1) (b) 4y +16% 5 = 0, sins) (a) y: (Simplify your answer. Type your answer in slopeiintercept form. Use integers or fractions for any numbers in the expression.) (bi y = (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.) In each case determine k so that the line is parallel to the line 2x - 5y + 37 =0. (a) y = kx + 5 (b) x = ky + 5 (a) What value of k will make y = kx + 5 parallel to 2x - 5y + 37 = 0? K= (Simplify your answer. Type an integer or a fraction.) (b) What value of k will make x = ky + 5 parallel to 2x - 5y + 37 = 0? K= (Simplify your answer. Type an integer or a fraction.)Classify the role ofthe variables as one ofthe following types: generalized; expressing a relationship; expressing a formula, or an unknown {3} To construct a square garden with an area of 50 square meters, the length; a, of each side must satisfy a2 = 50. {b} Sandra spends $D to make lots of lemonade and sells it for 50 cents a cup. If she sells L cups then her prot is .5L D. {a} The variable plays the role of Y . {bl The variables play the role of Y . Complete parts (a) through (c) below. (a) Find two points on the line 10x + 2y = 12. Select all that apply. (b) Use the two points found in part (a) to calculate the slope m. (c) Solve the equation in part (a) for y in terms of x and thereby again determine the slope of the line, as well as the y-intercept. (Hint: Solving for y in terms of x gives the line.) . . . (a) Find two points on the line 10x + 2y = 12. Select all that apply. A. (5, -19) B. (6,36) c. (-1, -1) D. (-1,11) (b) Use the two points found above to calculate the slope m. m =(Type an integer or a fraction.) (c) Solve the equation in part (a) for y in terms of x and thereby again determine the slope of the line, as well as the y-intercept. (Hint: Solving for y in terms of x gives the line.) The equation of the line is y = (Simplify your answer.) Use the equation found above to determine the slope and y-intercept. The slope is and the y-intercept is (Type an integer or a fraction.)Compute the distance between the points. (13, 14) and ( - 2,6) The distance between the given points is (Type an exact answer, using radicals as needed.)