Pre - Calculus Math Help?

Question

Please help me with this problem and explain each step

Problem:

During one week, the school bookstore made a profit of $546 when 91 students bought something from the store. The next week, the store made a profit of $496 when 86 students purchased something. Write the equation relating profit as a function of the number of students.

Answer 1

Use the points (91,546) and (86,496) and write the equation of a line in slope-intercept form.

Slope = difference of the y's over difference of the x's:

difference of the y's: 546-496=50

difference of the x's: 91-86=5

Slope=50/5 or 10

Find the y-intercept:

546=10*91+b

546=910+b

-364=b

y=10x-364

Or, to put it in terms of profit (p) and students (s),

p=10*s-364

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