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Answer :
Final answer:
The cost to install a swimming pool as a function of its area can be modeled by the linear equation y = 35x + 15,000, where y is the cost and x is the area in square feet. The cost increases by $35 per extra square foot of area.
Explanation:
The first step in modelling this scenario is to identify the slope of the linear relationship between the pool's area and its cost. The slope can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
Where:
Applying these numbers to the formula gives a slope (m) equal to $35 per square foot.
Next, we can determine the y-intercept (b) of the equation by substituting one of the points and the calculated m into the equation y = mx + b:
$50,000 = $35 * 1000 + b, solving for b gives b = $15,000.
Therefore, the linear equation that models this situation is y = 35x + 15,000. The graph of this equation is a straight line that starts at (0, 15,000) and increases with a slope of 35. Every increase in pool area of 1 square foot increases the cost by $35.
Learn more about Linear Function here:
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