Question

this model is of the form f(x) = mx + b. determine what m and b signify. 8) the cost, in dollars, of cellular phone service with econo-phone is given by c(x) = 0.62x + 31.50, where x is the number of minutes used in one month.

Explanation:

Step1: Analyze the slope (m)

In the linear cost function \( C(x) = mx + b \), the coefficient of \( x \) (which is \( m \)) represents the rate of change of the cost with respect to the number of minutes used. For \( C(x)=0.62x + 31.50 \), \( m = 0.62 \). This means that for each additional minute of phone service used (\( x \) increases by 1), the cost \( C(x) \) increases by \( \$0.62 \). So \( m \) is the cost per minute of cellular phone service.

Step2: Analyze the y - intercept (b)

The constant term \( b \) in the linear function \( C(x)=mx + b \) is the value of the function when \( x = 0 \). When \( x = 0 \) (no minutes of phone service used in the month), \( C(0)=0.62(0)+31.50 = 31.50 \). So \( b = 31.50 \) represents the fixed cost of the cellular phone service per month (the cost even when no minutes are used, perhaps a base fee or monthly service charge).

Answer:

• \( m = 0.62 \) signifies that the cost of cellular phone service increases by \(\$0.62\) for each additional minute used. (In other words, \( m \) is the cost per minute of cellular phone service.)
• \( b = 31.50 \) signifies the fixed monthly cost of the cellular phone service (the cost when \( 0 \) minutes are used, like a base or monthly service fee).