Question

At o degrees Celsius, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of gas increases by two twenty fifths. Write an equation that represents the volume of the gas in terms of the temperature.

Answer 1

`V=(2)/(25)T+22`

Explanation:

It is given that,

At 0 degrees Celsius, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of gas increases by 2/25.

If we take a cartesian coordinate, the line passes through (0,22). The slope of the line is 2/25.

The equation of a point-slope form is given by :

`y-y_1=m(x-x_1)\\\\y-22=(2)/(25)(x-0)\\\\y-22=(2x)/(25)\\\\y=(2x)/(25)+22`

Here, x will be temperature and y will be volume. So,

`V=(2)/(25)T+22`

Hence, the equation that represents the volume in terms of the temperature is
`V=(2)/(25)T+22`