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Chapter 2: Problem 1

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(4,7)\( and \)(8,10)$$

Short Answer

Expert verified
The slope of the line passing through the points (4,7) and (8,10) is 3/4. The line rises.

Step by step solution

01

Identify the Coordinates

The coordinates given in the problem are (4,7) and (8,10). We can let (4,7) be \((x1, y1)\) and (8,10) be \((x2, y2)\).
02

Apply the Slope Formula

Now we can substitute these coordinates into the slope formula, which is \((y2 - y1) / (x2 - x1)\). This gives us: \((10 - 7) / (8 - 4)\) = 3 / 4.
03

Find the Description of the Line

Since 3 / 4 is a positive number, it can be inferred that the line rises. Also, it's not 0, so we know the line isn't horizontal. And since it's defined (we can calculate it without getting an error), it's not a vertical line.

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