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 is:

• 
  `y = 15x+210`

Explanation:

The slope-intercept form of the line equation

y = mx+b

where m is the rate of change or slope and b is the y-intercept

Given

• 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

• so, the rate of change or slope = m = 15

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

i.e. (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`

Thus, the y-intercept b = 210

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

`y = mx+b`

`y = 15x+210`

Hence, an equation in the slope-intercept form is:

• 
  `y = 15x+210`