Question

Jaycie has 21 gallons of gas in her car and uses approximately .05 gallons of gas each mile that she drives. Which equation shows the linear relationship between x, the number of miles Jaycie has driven, and y, the total gallons of gas in her car? a. Y = 21x - .05 b. Y = -.05(x+21) c. Y = 21 - .05x d. Y =21 + .05x

Answer 1

Given:

Jaycie has 21 gallons of gas in her car and uses approximately .05 gallons of gas each mile that she drives.

To find:

The equation which shows the linear relationship between x, the number of miles Jaycie has driven, and y, the total gallons of gas in her car.

Solution:

We have,

Initial amount of gas in car = 21 gallons

So, y-intercept of the linear relationship is 21.

It uses approximately .05 gallons of gas each mile that she drives.

It means, the gas is decreased by .05 gallons for each mile.

So, slope of the linear relationship is -0.05. Here, negative sign represents the decrease in amount of gas.

Slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept or initial value.

Substitute m=-.05 and b=21 in the above equation.

$y=-.05x+21$

$y=21-.05x$

So, the equation $y=21-.05x$ represents the linear relationship between x, the number of miles Jaycie has driven, and y, the total gallons of gas in her car.

Therefore, the correct option is c.