The first graph is the solution for given table and the linear equation is y=3x+2.
<u>Step-by-step explanation:</u>
The linear equation of the line is y=mx+c.
where m is the slope and c is the y intercept.
The slope 

Choose two points (0,2) and(1,5).

y=3x+c.
To find the y-intercept value substitute (0,2) in the equation.
2=0+c.
c=2.
∴y=3x+2.
They are using two different functions.
Tell your math teacher that questions like these are loaded and should not be given as assignments.
Answer:
Slope: 2/3
Step-by-step explanation:
You have to first write the equation into slope-intercept form...
y = mx + b
So...
-2x + 3y = -6
becomes...
3y = 2x - 6
y = 2/3x - 2
Which means...
2/3 is the slope
Hope this help :)
Let me know if there are any mistakes!!