Question

At the beginning of the year Monica puts a set amount of money into her health benefit account. Every month she withdraws $15 from this account for her contact lenses. After 3 months she has $255 left in her account.

Write an equation in slope-intercept form to represent the relationship between the time that has passed and the amount of money left in Monica's account. Let x represent the time in months and y represent the amount of money remaining in the account.

Answer 1

An equation in the slope-intercept form will be:

• y = 15x+210

Explanation:

We know The slope-intercept form of the line equation

`y = mx+b`

where

• m is the rate of change or slope

• b is the y-intercept

Let x represent the time in months

Let y represent the amount of money remaining in the account.

Given that every month Monica withdraws $15 from this account for her contact lenses

Thus, the rate of change or slope = m = 15

Given that after 3 months she has $255 left in her account.

So, we take the point (3, 255)

substituting m = 15, x = 3 and y = 255 in the slope-intercept form to determine the y-intercept

y = mx+b

255 = 15(3) + b

switch sides

15(3) + b = 255

45 + b = 255

b = 255 - 45

b = 210

Now, substituting m = 15 and b = 210 in the slope-intercept form of the line equation

y = mx+b

y = 15x+210

Therefore, an equation in the slope-intercept form will be:

• y = 15x+210