Problem 3
Question
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)$$
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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.
2Step 2: 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 \(m = \frac{{2 - 1}}{{2 - (-2)}}\).
3Step 3: Calculate the Slope
Solving it, \(m = \frac{{1}}{{4}}\). This is the slope of the line passing through the points.
4Step 4: Determine the Direction of the Line
Since the slope is positive, the line rises from left to right.
Other exercises in this chapter
Problem 2
Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(5,1) \text { and }(8,5)$$
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