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Chapter 2: Problem 3

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. $$(-2,1)\( and \)(2,2)$$

Short Answer

Expert verified
The slope of the line passing through these points is \(\frac{1}{4}\). Because the slope is positive, the line rises from left to right.

Step by step solution

01

Identify the Given Points

The given points are (-2,1) and (2,2). Labelling these, let point 1, \(P_1\) be (-2,1) i.e. \(P_1(-2,1)\) and point 2, \(P_2\) be (2,2), i.e. \(P_2(2,2)\). The first number in each pair represents the x-coordinate while the second number represents the y-coordinate.
02

Apply the Slope Formula

The slope \(m\) is given by the formula \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\). Substituting our points into the formula gives \(m = \frac{{2 - 1}}{{2 - (-2)}}\).
03

Calculate the Slope

Solving it, \(m = \frac{{1}}{{4}}\). This is the slope of the line passing through the points.
04

Determine the Direction of the Line

Since the slope is positive, the line rises from left to right.

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Most popular questions from this chapter

Explain how to derive the slope-intercept form of a line's equation, \(y=m x+b,\) from the point-slope form \(y-y_{1}=m\left(x-x_{1}\right)\)

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