GianniJ2207
contestada

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.

Respuesta :

absor201

Answer:

An equation in the slope-intercept form is:

  • [tex]y = 15x+210[/tex]

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 [tex]m = 15[/tex], [tex]x = 3[/tex] and [tex]y = 255[/tex] in the slope-intercept form to determine the y-intercept

[tex]y = mx+b[/tex]

[tex]255 = 15(3) + b[/tex]

switch sides

[tex]15(3) + b = 255[/tex]

[tex]45 + b = 255[/tex]

[tex]b = 255 - 45[/tex]

[tex]b = 210[/tex]

Thus, the y-intercept b = 210

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

[tex]y = mx+b[/tex]

[tex]y = 15x+210[/tex]

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

  • [tex]y = 15x+210[/tex]

Otras preguntas