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Question 569548: I'm in a study hall right now and I've gone to the math wing to ask for help but they're in a meeting. my question is, Find the slope of f(x) where 2 <(or equal to) x <(or equal to) 10. There's a graph with this problem but I don't know how I'd show it to you. Thanks!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! There are a number of considerations in this problem. Do you know how to determine slope of a graph? Do you understand inequalities? Do you know what f(x) means? I'm not sure which of these is causing you difficulty.
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As far as the inequality is concerned, all that  is telling you is that the portion of the graph you are being asked about is where the graph is above region of the x-axis between x = +2 and x = +10 (and all values in between those two limits). Forget about portions of the graph anywhere else because the problem does not want an answer for them. It only asks you to find the slope of the graph where the value of x along the x-axis is greater than (or equal to) +2 and less than (or equal to 10).
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f(x) is the formula that converts the value of x into a value for y. Although it is not strictly mathematically correct, you can often think of replacing f(x) by y. For example, if you are told:
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f(x) = 2x + 3
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You can think of this as being:
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y = 2x + 3
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And this may be a little easier for you to work with since that's may be the way you began to work with solving equations and graphing them.
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Finding the slope means finding the change in y divided by the change in x. Keep in mind that if the graph is rising (meaning y is getting bigger) as the value of x moves to the right along the x-axis, the slope is positive (+). But if the graph is going down as x moves to the right along the x-axis, the slope is negative (-).
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I am going to assume that the graph you were given is a straight line in the region where x has values of +2 and +10 or any value between those two numbers. If so, then look at the corresponding value of y when x is +2. Next find the corresponding value of y when x is +10. Then you can write the equation:
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Where the subscript identifies the value at the value of the subscript on the x-axis. I hope this isn't confusing. Here's a little better explanation:
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 means the value of x at the point 10 on the x-axis. Obviously this is just +10.
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 means the value of x at the point 2 on the x-axis. It is just 2
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 is the value of y that is above (or below) the 10 on the x-axis. Look on the graph to get this value.
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Finally,  is the value of y that is above (or below) where x is 2 on the x-axis.
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Just substitute these 4 numbers into the equation for the slope as below:
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The substitutions in the denominator are the ones that you know. And since 10 minus 2 is 8, this simplifies the slope equation to:
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Then you get the corresponding values for y from the graph, substitute them, and solve for the slope.
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I hope this quick explanation helps you to see your way through to an answer. If it does not, post your problem again. And, if you can, be a little more specific about where you are having difficulty understanding it.
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