SOLUTION: I need help on this problem. Find the equation of the line passing through the given points. Use function notation to write the equation. (2,6) and (3,11)

Algebra ->  Linear-equations -> SOLUTION: I need help on this problem. Find the equation of the line passing through the given points. Use function notation to write the equation. (2,6) and (3,11)      Log On


   

Question 838059: I need help on this problem.
Find the equation of the line passing through the given points. Use function notation to write the equation. (2,6) and (3,11)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
"Use function notation to write the equation" means that the answer should be written as
f(x) =... instead of y=... .
The function would be of the form f%28x%29=mx%2Bb with constants
m = slope of the line, and
b = y-intercept of the line

The points tell you that
f%282%29=6 and f%283%29=11 ,

In general,
you can substitute and solve as a system of equations, or
you can calculate the slope, and then decide how to figure out the function from then on.

You can calculate the slope as the change in y-coordinates divided by the change in x-coordinates:
m=%2811-6%29%2F%283-2%29 --> m=5%2F1 highlight%28m=5%29
That was easy.

From there, substituting the value for m and the coordinates of one of the points (chose one), lets you find b easily:
system%28f%28x%29=mx%2Bb%2C+m=5%2Cf%282%29=6%29--> 6=5%2A2%2Bb --> 6=10%2Bb --> 6-10=b --> highlight%28b=-4%29

Now we have highlight%28f%28x%29=5x-4%29 .

Verification:
It is a good idea to plug in x=2 and x=3 in there to verify that you get f%282%29=6 and f%283%29=11 .