Question

HELP! 40 POINTS


Tim explained a function in words and Paul wrote an equation.
Tim
The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it.
Paul
y – 1,400 = 56 (x + 26)
Whose function has the smaller y-intercept?

Tim’s with a y-intercept of $2,700
Paul’s with a y-intercept of $2,856
Paul’s with a y-intercept of $2,800
Tim’s with a y-intercept of $2,780

Answer 1

Tim’s function has the smaller y-intercept at $2780.

Tim’s function:

The equation for a straight line has the form y = mx + b.

b = $225/mo, so y = 225x + b

When x = 8 mo, y = $4580, so

$4580 = $225/mo × 8 mo  +b

b = $4580 - $1800 = $2780

∴ y = 225x + 2780

When x = 0, y = 2780. Tim’s y-intercept is $2780.

Paul’s function

y – 1400 = 56 (x + 26)

When x = 0,

y – 1400 = 56 × 26 = 1456

y = 1456 + 1400 = 2856. Paul’s y-intercept is at $2856.

Tim has the smaller y-intercept at $2780.