Answer :
The solution to the question are
- The equation of the line is y = -10x + 100
- The interpretation of the slope is that the battery reduces by 10% each hour
The equation of the relationship
The given parameters from the question are:
- (x, y) = (0, 100), (2, 80) and (4, 60)
- Relation type = linear relation
To calculate the equation of the relationship, we need to first calculate the slope
The slope of the relation is calculated using the following slope formula
m = (y₂ - y₁)/(x₂ - x₁)
In this case, we have
m = Slope
(x₁, y₁) = (0, 100),
(x₂, y₂) = (4, 60)
Substitute the known values in the equation
m = (100 - 60)/(0 - 4)
Evaluate the quotient
m = -10
The equation of the relation is represented using the following linear equation
y = m(x - x₁) + y₁
Where
m = -10 and (x₁, y₁) = (0, 100),
Substitute the known values in the equation
y = -10(x - 0) + 100
Evaluate
y = -10x + 100
The explanation of how to get the equation
The following steps are taken when the equation is being calculated
- Calculate the slope
- Use the slope and one of the points to calculate the linear equation
The interpretation of the slope
In part (a), we have the slope to be
m = -10
The question implies that the graph is the graph of the percentage of battery left after x hours
This means that the slope represents the percentage of battery that reduces each hour i.e. 10%
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