SOLUTION: 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

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

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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

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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.

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