Question

you are told that a bank investment can be modeled by a linear equation. the slope of the linear equation is positive and the value for b in the equation is 30,000. what can be said about the initial investment, and is the money increasing or decreasing, based on the information given?

Explanation:

Step1: Recall linear equation form

A linear equation is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. In the context of a bank investment, when \( x = 0 \) (initial time, or the start of the investment), \( y=b \). So here, when \( x = 0 \), \( y=30000 \), which means the initial investment is $30,000.

Step2: Analyze the slope's meaning

The slope \( m \) of the linear equation is positive. In the context of a bank investment model \( y=mx + b \), where \( y \) represents the amount of money in the investment and \( x \) represents time (or some other variable related to the growth of the investment), a positive slope means that as \( x \) (time or the relevant variable) increases, \( y \) (the amount of money) also increases. So the money in the investment is increasing.

Answer:

The initial investment is $30,000, and the money is increasing.