1) What is the equation, in point-slope form, for a line that goes through (8,−4) and has a slope of −5/6 ?y+4=−5/6(x−8)y−4=−5/6(x−8)y+4=−5/6(x+8)y−4=−5/6(x+8)2)What is the equation of a line, in point-slope form, that passes through (−8, 1) and has a slope of 5/6 ?y+1=5/6(x−8)y+8=5/6(x−1)y−8=5/6(x+1)y−1=5/6(x+8)3) What is the equation in point-slope form of the line that passes through the points (7,5) and (−4,−1) ?y−1=6/11(x−4)y+4=11/6(x+1)y+1=6/11(x+4)y+1=6/7(x+4)4) What is the equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9) ?y+3=−2(x−5)y+3=−12/7(x−5)y−3=−2(x+5)y−3=−12/7(x+5)5) Plot the line for the equation on the graph.y−4=−1/4(x−5)

Answer:The answers are:1)  y + 4 = -5/6(x - 8), which is A, the first option.2)  y - 1 = 5/6(x + 8), which is D, the last option.3)  y + 1 = 6/11(x + 4), which is option C, the third option4) - y + 3 = -12/7(x - 5), which is option B, the second from the top5) Plot these points on a graph:(-1, 5 1/2)(0, 5 1/4)(1, 5)(2, 4 3/4)Step-by-step explanation:Question 1:y - y1 = m(x - x1)y - (-4) = -5/6(x - 8)y + 4 = -5/6(x - 8), which is A, the first option.Question 2:y - y1 = m(x - x1)y - 1 = 5/6(x - (-8))y - 1 = 5/6(x + 8), which is D, the last option.Question 3:m = (y - y1)/(x - x1)m = (5 - (-1)) / (7 - (- 4))m = (5 + 1) / (7 + 4)m = 6 / 11Use the point slope equation and (-4, -1), substitute:y - y1 = m(x - x1)y - (-1) = 6/11(x - (-4))y + 1 = 6/11(x + 4), which is option C, the third optionQuestion 4:m = (y - y1)/(x - x1)m = (-3 - 9)/(5 - (- 2))m = -12 / (5 + 2)m = -12/7Use the point slope equation and (5, -3), substitute:y - y1 = m(x - x1)y - (-3) = -12/7(x - 5)y + 3 = -12/7(x - 5), which is option B, the second from the topQuestion 5:Solve for y, then calculate a few points, graph those points:y - 4 = -1/4(x - 5)y - 4 = -1/4x + 5/4y = -1/4x + 5/4 + 4y = -1/4x + 5/4 + 16/4y = -1/4x + 21/4Solve for x =  -1, 0, 1, 2:f(-1) = -1/4(-1) + 21/4 = 1/4 + 21/4 = 22/4 = 5 1/2, giving point (-1, 5 1/2)f(0) = 21/4 or 5 1/4 giving point (0, 5 1/4)f(1) = -1/4 + 21/4 = 20/4 = 5, giving point (1, 5)f(2) = -1/4(2) + 21/4 = -2/4 + 21/4 = 19/4 or 4 3/4, giving point (2, 4 3/4)