|
Question 83960: Interest rates. A credit manager rates each applicant for a car loan on a scale of 1-5 and then determines the interest rate from the accompanying table. Find the equation of the line in slope-intercept form that goes through these points.
Credit rating Interest rate (%)
1 24
2 30
3 16
4 12
5 8
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since the equation we want is a line, we can use any 2 points to find the equation. So lets use (1,24) and (2,30)
| Solved by pluggable solver: Finding the Equation of a Line |
First lets find the slope through the points ( , ) and ( , )
 Start with the slope formula (note: ( , ) is the first point (,) and ( , ) is the second point (,))
 Plug in  , , , (these are the coordinates of given points)
 Subtract the terms in the numerator  to get  . Subtract the terms in the denominator  to get
So the slope is
------------------------------------------------
Now let's use the point-slope formula to find the equation of the line:
------Point-Slope Formula------
 where  is the slope, and (,) is one of the given points
So lets use the Point-Slope Formula to find the equation of the line
 Plug in , , and (these values are given)
 Distribute
 Multiply and  to get  . Now reduce to get 
 Add to both sides to isolate y
 Combine like terms and to get 
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line which goes through the points (,) and (,) is:
The equation is now in  form (which is slope-intercept form) where the slope is and the y-intercept is 
Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)
 Graph of through the points (,) and (,)
Notice how the two points lie on the line. This graphically verifies our answer.
|
|
|
|
| |
