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

Answer:

An equation in the slope-intercept form is:

• $y = 15x+210$

Step-by-step 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:

• $y = 15x+210$