Formula in the form y=mx+b models the value, y, of a new car x years after the initial purchase in 2010. Would you expect b to be positive, negative, or zero?

The equation of a line modeling the price of a car over the years from its initial purchase is to be a line with negative slope "m" due to the fact that the price of the car drops with the years, but for sure the price at the time of purchase (which is the zero in the horizontal x-axis) should be the largest value the car would have (the purchase price) This is actually the y-intercept "b", clearly a positive number.

astha8579 astha8579 · Answer 2 · 2022-03-04T12:28:06+01:00

The value of b for the given equation is expected to be positive

How to model a situation using a linear equation?

If the relationship between two variables is approximately going linear, then linear equation of the form [tex]y = mx + b[/tex] can be used, specially when x is independent variable and y in dependent variable.

b is some specific constant value for a relationship, called as y-intercept.

For the given case, we are given that:

x = years passed after 2010
y = price of the cars after x years passed.

As the value of x will increase the value of y should go on decreasing.

Analyzing the linear relationship between x and y, we see that [tex]y = mx + b[/tex] will result low values of y if m is negative.

Now since mx is negative, b must be positive as y cannot go smaller than 0.

Also, b can model the price of the car back in 2010 and that [tex]mx[/tex] would be the price that is being deduced after x years.

Thus, the value of b for the given equation is expected to be positive

Learn more about linear equations here:

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