Question

assume that a linear equation models the situation.
the total cost of a person’s cell phone was $585 after 6 months of service and $1010 after 11 months. what costs had he already incurred when her service had just begun? assume that her monthly charge is constant.
when the service had just begun, the total cost of $\square had already been incurred.

Explanation:

Step1: Define variables and linear equation

Let \( x \) be the number of months and \( y \) be the total cost. The linear equation is \( y = mx + b \), where \( m \) is the monthly charge (slope) and \( b \) is the initial cost (y-intercept, which we need to find). We have two points: \( (6, 585) \) and \( (11, 1010) \).

Step2: Calculate the slope \( m \)

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points:
\( m=\frac{1010 - 585}{11 - 6}=\frac{425}{5} = 85 \)

Step3: Find the initial cost \( b \)

Use one of the points, say \( (6, 585) \), and substitute into \( y = mx + b \):
\( 585 = 85\times6 + b \)
\( 585 = 510 + b \)
Subtract 510 from both sides: \( b = 585 - 510 = 75 \)

Answer:

75