Question

You have an allowance to spend on lunch this week. You will spend the same amount each day, and you get to keep whatever is left at the end of the week. After two days, you have $12.10 remaining. After 5 days, you have $2.50 remaining. Write an equation in slope- intercept form.

Answer 1

Answer:

$y=-3.2x+18.5$

Step-by-step explanation:

Let

x ----> the number of days

y ----> the amount of money remaining in dollars

we have the points

(2,12.10) and (5,2.50)

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2.50-12.10}{5-2}$

$m=\frac{2.50-12.10}{5-2}$

$m=-3.2\ \ /day$  ----> is negative because is a decreasing function

step 2

Find the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

with the slope m and the point (2,12.10) find the value of b

substitute

$12.10=-3.2(2)+b$

solve for b

$12.10=-6.4+b$

$b=12.10+6.4$

$b=18.5$

substitute

$y=-3.2x+18.5$