WEBVTT
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Mathew rides his bike at a steady rate of 15 miles per hour.
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The function 𝑦 equals 15𝑥 shows how time 𝑥 relates to the distance 𝑦.
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Which graph represents this function?
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Well, first of all, we can say that the time is 𝑥 and the distance is 𝑦.
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So therefore, straight away, we can rule out graphs C and E.
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And that’s because they actually have their axes the other way, because we have our time at 𝑦-axis and we have our distance as our 𝑥-axis.
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So now we actually have three graphs left to choose from.
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And to enable us to do that, what we’re gonna have a look at is the fact that this is actually Matthew riding his bike at a steady rate.
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And therefore, as he’s actually riding his bike at a steady rate, we know this is gonna be a linear graph.
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Well, this doesn’t rule any graphs out.
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But it does give us something important, because we know that the equation of a straight line is 𝑦 equals 𝑚𝑥 plus 𝑐, given that 𝑚 is the slope and 𝑐 is the 𝑦 intercept.
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Well, if we look at our function, which is 𝑦 equals 15𝑥, first of all, we can see that there’s no 𝑐.
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So therefore, the 𝑦-intercept must be zero.
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Well, for the three graphs that are left, the 𝑦-intercept is actually zero on each of these, so doesn’t rule any out.
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But next, we’re gonna look at the slope.
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And the slope of our function is 15.
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So therefore, we need to find the graph that has a slope of 15.
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So the slope is equal to change in 𝑦 divided by change in 𝑥.
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Okay, so great!
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We now know what the slope is.
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Let’s try and find out whether any of our graphs have a slope of 15.
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Now because each of our graphs actually goes through the origin, it’s gonna be very easy for us to actually find out the slope of our graphs.
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As if they actually have a slope of 15, then they’re gonna go through the point one, 15.
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But if we look at graph A, we can see if we go one on the 𝑥-axis, then we get 15 on the 𝑦-axis.
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So this could be our graph.
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And it probably will be.
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But we’re gonna have a look at B and D just to make sure.
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But if we look at graph B and we go up at one in the 𝑥-axis, we actually get below 15 on the 𝑦-axis.
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So therefore, our slope will not be 15.
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And we can double-check this by using an 𝑥 value of two because it should give us a 𝑦 value of 30.
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And it doesn’t, actually gives us around 15.
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So therefore, this definitely does not have a slope of 15 and therefore cannot be our graph.
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So finally, we’re gonna look at graph D.
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And if we look at graph D, this is much to state because actually our 𝑥 value of one gives us a value much higher than 15.
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So therefore, the slope would be greater than 15.
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And therefore, we can say this isn’t our graph.
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So therefore, we can say that graph A represents the function 𝑦 equals 15𝑥.