Question

suppose the number of people y (in hundreds) employed as asteroid miners can be estimated by the linear equation ( y = 33x + 560 ), where x is the number of years after 2002.
a. graph the linear equation.
b. does the point ( (5,725) ) lie on the line? if so, what does this ordered pair mean?
a. choose the correct graph.
○ a.
○ b.
○ c.
○ d.

Explanation:

Step1: Analyze the slope and y - intercept

The linear equation is \(y = 33x+560\). The slope \(m = 33>0\), so the line is increasing. The y - intercept \(b = 560\).

Step2: Check the point \((5,725)\)

Substitute \(x = 5\) into the equation \(y=33x + 560\).

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Answer:

b. Yes, the point \((5,725)\) lies on the line. The ordered pair \((5,725)\) means that 5 years after 2002 (i.e., in 2007), the number of people employed as asteroid miners is 725 hundred (or 72500).

For part a, since the slope is positive (\(m = 33\)) and y - intercept \(b = 560\), we need to look for a graph that is increasing and crosses the y - axis at \(y = 560\). Without seeing the exact details of the graphs (but based on slope and intercept analysis):

• Option A and D have negative slopes (since the lines are decreasing), so they are incorrect.
• Between B and C, we know that when \(x = 0\), \(y=560\). If we assume proper scaling on the y - axis (where the y - intercept is around the middle - upper part of the y - axis range shown in the graphs), we would choose the graph (either B or C) that has a positive slope and y - intercept at \(y = 560\). But since we can't see the exact y - axis labels for B and C in detail from the text - based image, the key is that the correct graph has a positive slope and \(y(0)=560\).