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Chapter 3: 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. $$(-2,1) \text { and }(2,2)$$

Short Answer

Expert verified
The slope of the line is \(1/4\) and the line rises.

Step by step solution

01

Identify the given points and apply the slope formula

The given points are (-2,1) and (2,2). To calculate the slope, use the formula \(m = (y_2 - y_1) / (x_2 - x_1)\). The coordinates of the first point are \((-2,1) = (x_1,y_1)\) and the second point are \((2,2) = (x_2,y_2)\).
02

Substitute the values into the slope formula

Now, substitute the values of the coordinates into the slope formula. So \(m = (2 - 1) / (2 - -2)\).
03

Solve the expression

Simplify the expression obtain: \(m = 1/4\).
04

Interpret the Slope

Since the slope is positive, this means that the line rises.

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Most popular questions from this chapter

What is a \(y\) -intercept of a graph?

Make Sense? In Exercises \(70-73\), determine whether each statement "makes sense" or "does not make sense" and explair your reasoning. The slope-intercept form of a line's equation makes it possible for me to determine immediately the slope and the \(y\) -intercept.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line whose equation is \(y-3=7(x+2)\) passes through \((-3,2)\)

Simplify: \(3(1-2 \cdot 5)-(-28)\) (Section \(1.8,\) Example 7 )

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((2,4)\) and has the same \(y\) -intercept as the line whose equation is \(x-4 y=8\)
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