Answer :
To create an equation in slope-intercept form that models the amount owed
y after
x months for Diana's loan, we start with the following information:
Diana borrowed
$
700
$700.
She plans to make monthly payments of
$
70
$70.
The amount owed
y after
x months can be represented as follows:
Initial amount borrowed:
=
700
y=700
Amount paid off per month:
Diana pays
$
70
$70 per month.
Therefore, the amount the loan decreases each month is
$
70
$70.
Equation in slope-intercept form:
After
x months, the amount owed
y is reduced by
70
70x (since she pays off
$
70
$70 each month). Therefore, the equation can be written as:
=
700
−
70
y=700−70x
Interpretation of the equation:
y represents the amount of the loan still owed after
x months.
700
700 is the initial amount borrowed.
−
70
−70x accounts for the reduction in the loan amount due to the monthly payments of
$
70
$70.
Slope-intercept form:
The equation
=
700
−
70
y=700−70x is in slope-intercept form, where:
The slope
m is
−
70
−70, indicating that the amount owed decreases by
$
70
$70 per month.
The y-intercept
b is
700
700, which is the initial amount borrowed.
Therefore, the equation in slope-intercept form that models the amount owed
y of Diana’s loan after
x months is:
=
700
−
70
y=700−70x
