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 slope
b: It is the cut-off point with the y axis
According 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!
[tex](x, y) :( 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!
[tex](x, y) :( 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!
[tex](x, y): (- 3,7)\\7 = - \frac {2} {3} (- 3) + \frac {5} {3}\\7 = 2 + \frac {5} {3}\\7 = \frac {11} {3}[/tex]
It is not fulfilled!
[tex](x, y) :( 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]
