Answer: Hello mate!
we have a table with the pairs (2,48), (5,98), (12, 188) and (20,300)
we know that the model is a linear function, by looking at the given options, then we can obtain the slope in the next way:
for a function y(x) = ax + b, we can obtain the slope a in the next way:
[tex]a = \frac{y(x2) - y(x1)}{x2 - x1}[/tex]
Then we can obtain the slope on our situation with two pairs of the given ones; took (2,48) and (20,300) because are the two extremes of our set:
[tex]a = \frac{300 - 48}{20 -2} = \frac{252}{18} = 14[/tex]
Now lets find the x-intercept.
if y(x) = 14x + b, let's evaluate the pairs given and find the value of b.
y(2) = 48 = 14*2 + b
b = 48 - 28 = 20
and y(20) = 300 = 14*20 + b
b = 300 - 14*20 = 20
Then the correct answer is the option C.
You can see that this function is not 98 when x = 2, this can be a typo in the table, but this does not matter, because we are modeling the situation, which is giving an approximation, and this is just one point outside our lineal approximation.
You also can do linear regression in this problem, using something like origin, but I think that the eye approximation is a more useful skill to develop.
