Question

Vera wants to graph a line that passes through (0,2) and has a slope of 2/3 which points could Vera use to graph a line check all that apply

Answer 1

The line Vera is graphing has a slope of
`(2)/(3)` and passes through the point (0,2) that is m=
`(2)/(3)` and b=2.

The equation of the line is

`y=(2)/(3)x+2`

To find the points which will lie of the given line we substitute the x and y values in the equation.If both sides are equal then the point lies on the line.

1)(-3,0)

Substituting the values we have :

`0=(2)/(3)(-3)+2.`

0=-2+2

0=0

Point (-3,0) lies on the line.

2)(-2,-3)

Substituting the values :

`-3=(2)/(3)(-2)+2`

-3≠
`(2)/(3)`

Point(-2,-3) does not lie on the line.

3)(2,5)

`5=(2)/(3)(2)+2\\ 5\\eq 3`

Point (2,5) does not lie on the line.

4)(3,4)

`4=(2)/(3)(3)+2\\ 4=4`

Point (3.4) lie on the line.

5)(6,6)

`6=(2)/(3)(6)+2`

6=6

Point (6,6) lie on the line

The points that will lie on the line are (-3,0) (3,4)and (6,6)