suppose that the given line has a slope of -2/3 and a y-intercept of (0,5/3). which of the following points is also a solution to the line? select all apply A. (5,5/3) B. (1,1) C. (4,-1) D. (-3,7) E. (0,0)

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:[tex]y = mx + b[/tex]Where:m: It's the slopeb: It is the cut-off point with the y axisAccording to the data we have to:[tex]m = - \frac {2} {3}\\b = \frac {5} {3}[/tex]Thus, the equation is:[tex]y = - \frac {2} {3} x + \frac {5} {3}[/tex]We evaluate each point:[tex](x, y) :( 5, \frac {5} {3})[/tex][tex]\frac {5} {3} = - \frac {2} {3} (5) + \frac {5} {3}\\\frac {5} {3} = - \frac {10} {3} + \frac {5} {3}\\\frac {5} {3} = - \frac {5} {3}[/tex]It is not fulfilled :( 1,1)\\1 = - \frac {2} {3} (1) + \frac {5} {3}\\1 = - \frac {2} {3} + \frac {5} {3}\\1 = \frac {3} {3}\\1 = 1[/tex]Is fulfilled :( 4, -1)\\-1 = - \frac {2} {3} (4) + \frac {5} {3}\\-1 = - \frac {8} {3} + \frac {5} {3}\\-1 = - \frac {3} {3}\\-1 = -1[/tex]Is fulfilled: (- 3,7)\\7 = - \frac {2} {3} (- 3) + \frac {5} {3}\\7 = 2 + \frac {5} {3}\\7 = \frac {11} {3}[/tex]It is not fulfilled :( 0,0)\\0 = - \frac {2} {3} (0) + \frac {5} {3}\\0 = \frac {5} {3}[/tex]NOT fulfilled!Answer:The points that belong are:[tex](1,1); (4, -1)[/tex]