Question

Analyse the table of values. The variable, T, represents the quantity (L) of gas in a tank and the variable, d, represents the distance travelled (km). What is the rate of change? Show calculations. Describe what this rate means in the real world? Graph this relation. Extrapolate to discover how far the vehicle travels before the tank is empty.

Answer 1

The answer is below

Explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

a) d is on the x axis and T is on the y axis, the rate of change is gotten using the points (0, 75) and (300, 37.5). Hence the rate of change (m) is:

`m=(y_2-y_1)/(x_2-x_1) =(37.5-75)/(300-0) =-0.125`

b) The rate of change means that the quantity of gas in tank decreases by 0.125 for every km traveled.

c) The graph was plotted using geogebra online graphing tool.

d) Using the points (0, 75) and (300, 37.5), the equation of the line is:

`T-T_1=(T_2-T_1)/(d_2-d_1)(x-x_1) \\\\T-75=(37.5-75)/(300-0)(d-0)\\\\T=-0.125d+75`

The tank is empty when T = 0, hence:

0 = -0.125d + 75

0.125d = 75

d = 600 km

The tank is empty at 600 km