SOLUTION: Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from 65 to 95. Let “x” be an original score, and “y” be

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Question 335606: Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from 65 to 95. Let “x” be an original score, and “y” be a curved score. Using the ordered pairs (30,65) and (70,95), write the equation in slope/intercept form that she should use to curve the test scores.
In the scenario given above, what will an original score of 62 become?
I could really use some help with this. Any help would be really appreciated!!!
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start with the "slope-intercept" form of a linear equation.
y = mx+b where m is the slope and b is the y-intercept.
We can calculate the slope, m, using the two given points (30,65) and (70,95) as follows:
m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
The x's and the y's here are taken from the two points.
m+=+%2895-65%29%2F%2870-30%29
m+=+30%2F40
m+=+3%2F4 so now we can write...
y+=+%283%2F4%29x%2Bb To find the value of b, we'll use the x- and y-coordinates from either one of the two given points. Let's use (30,65).
65+=+%283%2F4%29%2830%29%2Bb Simplify.
65+=+%2890%2F4%29%2Bb Simplify the fraction.
65+=+%2845%2F2%29%2Bb Multiply everything by 2 to clear the fraction.
130+=+45%2B2b Subtract 45 from both sides.
85+=+2b divide both sides by 2.
b+=+42.5
Now we can write the final equation in slope-intercept form:
highlight%28y+=+%283%2F4%29x%2B42.5%29
Let's see how that looks when graphed:
graph%28400%2C400%2C-5%2C100%2C-5%2C100%2C%283%2F4%29x%2B42.5%29

Answer by Edwin McCravy(8909) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is the same as if it had read: 

"Find the equation of a line that passes through the two points

(30,65) and (70,95), then find the y-coordinate of the point that

has x-coordinate 62."

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%2895-65%29%2F%2870-30%29=30%2F40=3%2F4

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-65=%283%2F4%29%28x-30%29

y-65=%283%2F4%29x-45%2F2

y=%283%2F4%29x-45%2F2%2B65

y=%283%2F4%29x-45%2F2%2B+130%2F2

y=%283%2F4%29x%2B85%2F2

Plug in x=62

y=%283%2F4%29%2862%29%2B85%2F2

y=93%2F2%2B85%2F2

y=178%2F2

y=89

Edwin