Question

What is the equation of the line connecting (1,5) and (4,14)?

Answer 1

To find the slope of the line:
(y2-y1)/(x2-x1)
(14-5)/(4-1)=(9)/(3)=3

Only one of your 4 possible answers has 3 as a slope. However, plugging in each point into the y=mx+b equation, the y-intercept consistently comes out as 2..
y=mx+b
14=3(4)+b  b=2
5=3(1)+b    b=2
y=3x+2
If there is a consistent, positive slope (from your question, this does not seem to have a quadratic as an option), 3x+5 is not even a viable solution because x=1 when the y-value is 5 (and thus no other x value {0} could have a y-value of 5). It seems as though you have a typo on your hands. Hopefully this helps?