Question

Write an equation that represents the relationship between the independent and dependent quantities listed in the table. The table reads as follows:

Input (x) 1 2 3 4
————
output (y) 3 5 7 9

Answer 1

First, we can note that the relation between the independent and the dependent variables is a linear relation.

We will need two points: (1,3) and (2,5)
The general form of the equation of the linear line is:
y = mx + c where m is the slope and c is the y-intercept

To get the slope, we will use the following rule:
m = (y2-y1) / (x2-x1)
m = (5-3) / (2-1) = 2
The equation of the line now becomes:
y = 2x + c

To get the value of the c, use any of the given points and substitute in the equation. I will use (1,3) as follows:
y = 2x + c
3 = 2(1) + c
c = 3-2 = 1

Therefore, the equation of the line is:
y = 2x + 1