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

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)

To find the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Take the first two points \((2, 145)\) and \((4, 215)\).
\( m=\frac{215 - 145}{4 - 2}=\frac{70}{2}=35 \).

Step2: Find the y-intercept (b)

Use the slope-intercept form \( y = mx + b \) and substitute \( m = 35 \), \( x = 2 \), \( y = 145 \).
\( 145 = 35(2) + b \)
\( 145 = 70 + b \)
Subtract 70 from both sides: \( b = 145 - 70 = 75 \).

Step3: Form the equation

With \( m = 35 \) and \( b = 75 \), the equation is \( y = 35x + 75 \).

Answer:

D. \( y = 35x + 75 \)