Can anyone please help with how to estimate and interpret the intercepts of a graph for the attached image?  Thanks!

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

Based on the given graph, it goes up from left to right, so the slope is positive.

Since the graph goes up from left to right it means that as x increases y also increases.

The independent variable here is x, and the dependent variable is y.

The x will be the number of shirts and the y will be the total cost, take note that the total cost depends on the number of shirts you buy.

Therefore, as the number of shirts increases, the total cost also increases.

To show the relationship, based on the graph for 4 dozen shirts the total cost is $300

While, for 6 dozen shirts the total cost is $400.

mathscihelp's profile pic

mathscihelp | College Teacher | (Level 2) Adjunct Educator

Posted on

In problems like this one, one needs to carefully consider the relevance of the x-intercept and y-intercept within the context of the real-world problem. This graph describes the total cost in dollars, y, associated with the number of shirts (dozens), x, for a wholesale t-shirt order. y is the dependent variable, whereas x is the independent variable.  Remember that the x-intercept is the point at which the line crosses the x-axis, whereas the y-intercept is the point at which the line crosses the y-axis. In this problem, ask yourself if you see such points. If so, what is their relevance? Let us first focus on the easy part. There does not appear to be a point that the graph crosses the x-axis which has relevance. We would have to have a negative number of shirts to make this so from the graph. This does not make sense. The values for x can only be greater than or equal to 0, not negative. Thus, we are left with considering only the y-intercept. It looks like the line touches the y-axis at a point between $200 and $0. Hmm. How can we “estimate” what this value is? Well, it looks like the y-axis is broken up into increments of $200 ($0, $200, $400, $600, $800, and $1000). The tick mark between $0 and $200 is at $100. Is the point at which the line crosses the y-axis above or below this point? It is below. Now we know that our target “estimate” is less than $100 but more than $0. To me, it looks this point is $50. Hmm. How do we interpret this result? Does this make sense? When zero shirts are sold, there is a total cost of approximately $50. How could this happen? I suspect that this cost is a fixed cost that the manufacturer has to pay regardless of the number of shirts that are sold.

Thanks for the great question! There is a lot of good mathematics going on.

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