Answer:
- 2x +3y = 36
- see the attachment for a graph
Explanation:
If we let x and y represent the numbers of small vans and large vans, respectively, then we know the equation will be of the form ...
8x +12y = (total number of people)
Standard form requires the coefficients not have any common factors, so we must divide by 4. One way to find the constant on the right is to start with a form of the equation that ensures it goes through the point (15, 2), the given numbers of vans the people fill. That looks like this:
2(x -15) + 3(y -2) = 0
Eliminating parentheses gives ...
2x -30 +3y -6 = 0
Consolidating the constant terms on the right makes our equation the one we're looking for:
2x +3y = 36
Attached is a graph of it.
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Comment on the graph
We have graphed it using a graphing calculator. If you want to graph it by hand, it is convenient to put the equation into intercept form:
x/(x-intercept) + y/(y-intercept) = 1
You can do that by dividing the standard form equation by the constant on the right:
2x/36 + 3y/36 = 1
and simplifying to intercept form ...
x/18 + y/12 = 1
This shows you the x-intercept of the graph is 18 small vans, and the y-intercept is 12 large vans. Drawing the line between these points gives you your graph.