The line Vera is graphing has a slope of [tex]\frac{2}{3}[/tex] and passes through the point (0,2) that is m=[tex]\frac{2}{3}[/tex] and b=2.
The equation of the line is
[tex]y=\frac{2}{3}x+2[/tex]
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 :
[tex]0=\frac{2}{3}(-3)+2.[/tex]
0=-2+2
0=0
Point (-3,0) lies on the line.
2)(-2,-3)
Substituting the values :
[tex]-3=\frac{2}{3}(-2)+2[/tex]
-3≠[tex]\frac{2}{3}[/tex]
Point(-2,-3) does not lie on the line.
3)(2,5)
[tex]5=\frac{2}{3}(2)+2\\ 5\neq 3[/tex]
Point (2,5) does not lie on the line.
4)(3,4)
[tex]4=\frac{2}{3}(3)+2\\ 4=4[/tex]
Point (3.4) lie on the line.
5)(6,6)
[tex]6=\frac{2}{3}(6)+2[/tex]
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)
