Question

Vera wants to graph a line that passes through (0, 2) and has a slope of . Which points could Vera use to graph the line? Check all that apply. (–3, 0) (–2, –3) (2, 5) (3, 4) (6, 6)

Answer 1

we have

1) The line passes through $(0,2)$

2) The slope is equal to $\frac{2}{3}$

we know that

If a point lies on the graph of the line, then the point must satisfy the equation of the line

Step 1  

Find the equation of the line

we know that

the equation of the line in point-slope form is equal to

$y-y1=m*(x-x1)$

we have

$(x1,y1)=(0,2)$

$m=\frac{2}{3}$

substitute in the equation

$y-2=\frac{2}{3}*(x-0)$

$y=\frac{2}{3}x+2$

we will proceed to verify each of the points to determine the solution of the problem

If a point lies on the graph of the line, then the point must satisfy the equation of the line and the equation will be true for the point

Step 2

Point $(-3,0)$  

Substitute the value of x and y in the equation of the line

$0=\frac{2}{3}*(-3)+2$

$0=-2+2$

$0=0$ -------> is true

therefore

the point  $(-3,0)$ lies on the line

Step 3

Point $(-2,-3)$    

Substitute the value of x and y in the equation of the line

$-3=\frac{2}{3}*(-2)+2$  

$-3=-\frac{4}{3}+2$  

$-3=\frac{2}{3}$ ------> is false  

therefore

the point $(-2,-3)$ not lies on the line

Step 4

Point $(2,5)$  

Substitute the value of x and y in the equation of the line

$5=\frac{2}{3}*(2)+2$  

$5=\frac{4}{3}+2$  

$5=\frac{10}{3}$ ------> is false  

therefore

the point $(2,5)$ not lies on the line

Step 5

Point $(3,4)$  

Substitute the value of x and y in the equation of the line  

$4=\frac{2}{3}*(3)+2$    

$4=2+2$  

$4=4$ ------> is True

therefore

the point $(3,4)$ lies on the line

Step 6

Point $(6,6)$        

Substitute the value of x and y in the equation of the line  

$6=\frac{2}{3}*(6)+2$    

$6=4+2$    

$6=6$ ------> is True

therefore

the point $(6,6)$ lies on the line

therefore

the answer is

Vera could use the points

the point  $(-3,0)$

the point $(3,4)$

the point $(6,6)$

using a graphing tool

see the attached figure to better understand the problem

Answer 2

A,D, AND E i just took the test.