The relationship between the number of gallons of gas that the car uses g, and the number of miles the car has driven d, is given by the equation g=0.04d. Since the values of g and d are linearly connected.
Which is said to be a Linear equation?
- A linear equation is an algebraic equation that has the highest degree as 1.
- The general form of the linear equation is [tex]y=ax+c[/tex]. Where y is the dependent variable and x is the independent variable.
- So, as the value of x increases the value of y also increases linearly and forms a straight line.
Given data:
It is given that,
A table of content about the distance traveled by Rachel and the gas used for that distance.
The distance is given in miles as d and the gas is given in gallons as g
The values of d given in the table are 14, 70, 109, and 140. Here the order is increasing.
The values of g given in the table are 0.56, 2.8, 4.36, and 17.6. Here also the order is increasing.
Finding the relationship between g and d:
Since the values of g and d are increasing linearly and g is depending on d, consider a linear equation as follows:
[tex]g=ad+c[/tex]
Finding a and c from the obtained equation:
From the table, when d=14, g=0.56 and d=70, g=2.8
On substituting these values in the equation we get
0.56=14a+c
2.8=70a+c
Subtracting 1st equation from the 2nd equation,
2.8-0.56=(70a+c)-(14a+c)
⇒ 2.24=56a
⇒ a=0.04
On substituting a value in any of the equations we get
0.56=(0.04)(14)+c
⇒ c=0
Thus, the required equation becomes g=0.04d. This says that the g and d values are linearly related to each other.
Learn more about linear equations here:
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