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Determine the slope of the line that passes through the points 𝐴: two, negative five and 𝐵: four, five.
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Slope is the ratio of the rise, which is the vertical change — the up and down change — to the run — the horizontal change moving left and right.
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So we are gonna find the slope that passes through these two points.
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Again, slope is the vertical change over the horizontal change.
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So if we imagine these two points on a graph, what would we have to look at for the vertical change?
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Well on a graph, the change going up and down is represented in the 𝑦-values.
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So we need to know the change between negative five to five.
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And when we try to find the change between two points, that’s like the difference between two points; how far apart are they?
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Well, we need to find the difference between them.
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So we have negative five minus five.
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The horizontal change is what moves left and right.
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Those would be your 𝑥-values on a graph.
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So for horizontal change, we need to look at the difference between the two and four; how far apart are they?
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We need to know difference between them.
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So right now, we have negative five minus five over two minus four.
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Negative five minus five is negative 10 and two minus four is negative two.
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Negative 10 divided by negative two is positive five because two negatives make a positive.
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Now when it comes to slope, again it’s the vertical change over the horizontal change.
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So instead of five, we should have five over one.
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That means we are going to rise five spaces and run one space.
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So we go up five and right one and then up five and right one and then up five and right one.
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The reason I say this is because in linear functions no matter which two points you would choose on a line, the slope, which is the rate of change, is always gonna stay the same.
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So if you’re going between these two points, the slope is gonna be five over one, and this is going to be a line.
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Well anywhere on that line, it’s gonna keep the same slope — five over one.
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So the slope of the line that passes through the points 𝐴: two, negative five and 𝐵: four, five would be five over one.