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The graph shows the capital of a company over eight years.
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Determine the slope of the line which represents the increase in capital in the first three years.
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This is a really nice question because it actually starts to talk about slope in a real-life context, which is good because it actually gets us to think about how it could be useful.
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The reason that slope can be useful when we’re looking at this real-life context, is that actually we waana see how quickly the capital increases or decreases over a set time.
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And for this question, it’s the first three years.
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As we’re looking at the first three years, it’s this section in the graph that we’re actually going to concentrate on when trying to solve this problem.
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So what does slope actually mean?
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Well, slope or 𝑚 is the change in 𝑦 divided by the change in 𝑥.
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So in this context, it’s gonna be our change in capital divided by our change in the number of years.
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To help us calculate slope, we actually have an equation which is 𝑚 is equal to 𝑦 two minus 𝑦 one divided by 𝑥 two minus 𝑥 one where 𝑦 one, 𝑦 two and 𝑥 one, 𝑥 two are actually the coordinates of two points on our line.
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When calculating the slope, you need to actually pick two points on your line cause actually if it’s a straight line, your slope will be the same throughout the whole length of that line.
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So it doesn’t really matter where you pick them, but do make sure they’re in a place where there is obvious values.
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So here we’ve already got 𝐴 and 𝐵 marked on our diagram.
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So we’ve got 𝐴 which is naught, 60 and 𝐵 which is three, 70.
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And now, I’m gonna label our coordinates.
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And I probably recommend you do this just until you’re really confident using the formula.
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Now we’ve labelled our coordinates, we can actually substitute our values into our formula.
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So first of all, we have 70 which is 𝑦 two minus 60 which is 𝑦 one divided by three which is 𝑥 two minus zero which is 𝑥 one.
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Great!
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So we’ve now subbed all of our values from our coordinates into our slope formula, and we can now solve this to find our slope.
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Fab!
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So we’ve now found the slope of our line, 𝑚 is equal to 10 over three or ten-thirds.
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And so therefore, we’ve solved the problem because what we’ve actually done, is we found the slope which represents the increase in capital in the first three years.
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And what that actually means in context, is actually over the first three years, our capital of the company has increased by 10000 pounds.