Read the following description of a relationship:A rancher is filling a trough for her horses. The trough already contained 18 gallons of water, and the rancher is adding 18 gallons per minute.Let m represent the number of minutes and g represent the number of gallons in the trough.This relationship can also be shown in a table. Complete the equation that represents the relationship between m and g.m g7 1448 1629 18010 198
Question
Read the following description of a relationship:A rancher is filling a trough for her horses. The trough already contained 18 gallons of water, and the rancher is adding 18 gallons per minute.Let m represent the number of minutes and g represent the number of gallons in the trough.This relationship can also be shown in a table. Complete the equation that represents the relationship between m and g.m g7 1448 1629 18010 198
Solution
The equation that represents the relationship between m (minutes) and g (gallons) is g = 18m + 18.
Here's how we get this:
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We know that the trough already contained 18 gallons of water. This is our starting point, so it's where the y-intercept of the equation comes from (the +18 in the equation).
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We also know that the rancher is adding 18 gallons per minute. This is our rate of change or slope, which is represented by 18m in the equation.
So, for every minute that passes (m), the rancher adds 18 gallons to the trough, and we add this to the initial 18 gallons that were already in the trough.
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