Answer:
[tex]y = \voxed{x + 3}[/tex]
Step-by-step explanation:
The table represents a linear relationship between y and x
If we graph the x, y values we will get a straight line
A straight line can be represented by the equation
y = mx + b
where m = slope = rate of change of y w.r.t x and b is the y-intercept where the line crosses the y-axis
Looking at the table we see that when x increases from 1 to 3(2 units), y also increases by 2 units from 4 to 6
When x increases from 3 to 12(9 units), y also increases by 9 units from 6 to 15
Therefore slope = 1 = m
In other words for every unit increase in x, y increases by 1 unit
The equation of the line is therefore
y = 1x + b
or
y = x + b
To find b, substitute a value for x and corresponding value for y and solve for b
Choose x = 1, y =4 the first entry
Plugging this in gives us
4 = 1 + b
b = 4 - 1 = 3
So the equation of the line is y = x + 3
