Question

cynthia put down a deposit for part of the cost of a new tv. she then paid an additional payment each month until the tv was completely paid for. the table represents the total amount she has paid, based on the number of months since she put down the deposit.

number of months	2	4	6	8	10
total paid ($)	145	215	285	355	425

which equation represents the relationship between the number of months, x, and the total amount she has paid?
a ( y = 70x + 145 )
b ( y = 70x + 75 )
c ( y = 35x + 145 )
d ( y = 35x + 75 )

Explanation:

Step1: Find the slope (rate of change)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \((2, 145)\) and \((4, 215)\):
\( m=\frac{215 - 145}{4 - 2}=\frac{70}{2}=35 \).

Step2: Use point - slope form to find the equation

Point - slope form is \( y - y_1=m(x - x_1) \). Using \( (2, 145) \) and \( m = 35 \):
\( y - 145=35(x - 2) \)
\( y - 145=35x-70 \)
\( y = 35x+75 \). We can check with another point, e.g., \( x = 6 \): \( y=35(6)+75 = 210 + 75=285 \), which matches the table.

Answer:

\( y = 35x + 75 \) (the option corresponding to this equation)