Please help me with these 5 questions!2. A. NoB. yes; k = -1/2 and y = -1/4xC. yes; k = 4 and y = 4xD. yes; k = 1/4 and y = 1/4x6.A. y = 5x-1B. y = 5/2x+5C. y = -x+5D. y = 1/5x-18. A. line aB. line dC. line bD. line c11. What is the slope of the line through the points (–2, –1) and (8, –3)?A. 3/2B. 1/5C. -3/2D. -1/515. A. line aB. line dB. line bC. line c

Accepted Solution

Answer:Part 2) Option D. yes; k = 1/4 and y = 1/4xPart 6) Option D. y = 1/5x-1Part 8) Option C. line bPart 11) Option D. -1/5Part 15) Option A. line aStep-by-step explanation:Part 2) we know thatA relationship between two variables, x, and y, represent a directly variation if it can be expressed in the form  [tex]y=kx[/tex] In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin In this problem the line passes through the originthereforeYes. y varies directly with xLetA(4,1)The constant k is equal to[tex]k=y/x[/tex] substitute[tex]k=1/4[/tex] the equation is equal to[tex]y=(1/4)x[/tex] Part 6) we know thatThe y-intercept of the trend line is -1 (For x=0)The slope of the trend line is positiveThe x-intercept of the trend line is 5 (For y=0)thereforethe equation is equal to[tex]y=(1/5)x-1[/tex]Part 8) we have[tex]y+4=-\frac{2}{3}x[/tex]This is the equation of a line into point slope formThe slope is negative [tex]m=-2/3[/tex]Pass through the point (0,-4) ----> y-interceptThe x-intercept is equal to[tex]0+4=-\frac{2}{3}x[/tex][tex]x=-4*3/2=-6[/tex]therefore Is the line bPart 11) What is the slope of the line through the points (–2, –1) and (8, –3)?we know that The formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute the values[tex]m=\frac{-3+1}{8+2}[/tex] [tex]m=\frac{-2}{10}[/tex] simplify[tex]m=-\frac{1}{5}[/tex] Part 15) we have[tex]y=3x-2[/tex]The slope is positive [tex]m=3[/tex]The y-intercept is -2 (For x=0)The x-intercept is  (For y=0)[tex]0=3x-2[/tex][tex]3x=2[/tex][tex]x=2/3[/tex]therefore the line is a