Question

Which equation represents the relationship shown in the table below?

A. y = –x – 3
B. y = x – 3
C. y = 2x − 3
D. y = ­­–2x + 3

Answer 1

The answer is C because every time you plug in the x-coordinate, the correct y-coordinate comes out. The last ordered pair is (3,3). When you plug in the 3, the equation is y=2(3)-3.  Multiply, and y=6-3.  Subtract and the answer is y=3, which is correct. This works for all the ordered pairs in this equation, so the equation is C: y=2x-3.

Answer 2

The generic equation of the line is:

`y = mx + b`
Where,
m: slope of the line
b: cut with the "y" axis
The slope is given by:

`m= (y2-y1)/(x2-x1)`
Substituting values:

`m= (3-1)/(3-2)`
Rewriting:

`m= (2)/(1)`

`m = 2`
The cut point occurs when x = 0. Therefore, from the table we observe that:

`b = - 3`
Substituting values we have:

`y=2x-3`
Answer:
C. y = 2x − 3