Question

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)

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data we have to:

`m = - \frac {2} {3}\\b = \frac {5} {3}`

Thus, the equation is:
`y = - \frac {2} {3} x + \frac {5} {3}`

We evaluate each point:

`(x, y) :( 5, \frac {5} {3})`

`\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}`

It is not fulfilled!

`(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`

Is fulfilled!

`(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`

Is fulfilled!

`(x, y): (- 3,7)\\7 = - \frac {2} {3} (- 3) + \frac {5} {3}\\7 = 2 + \frac {5} {3}\\7 = \frac {11} {3}`

It is not fulfilled!

`(x, y) :( 0,0)\\0 = - \frac {2} {3} (0) + \frac {5} {3}\\0 = \frac {5} {3}`

NOT fulfilled!

Answer:

The points that belong are:

`(1,1); (4, -1)`