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Chapter 3: Problem 4

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. $$(-1,3) \text { and }(2,4)$$

Short Answer

Expert verified
The slope of the line passing through the points (-1,3) and (2,4) is 1/3. Hence, the line through the points rises as the slope is positive.

Step by step solution

01

Identify The Given Points

The two points given are (-1,3) and (2,4). With these points, identify \( x_1 = -1 \), \( y_1 = 3 \), \( x_2 = 2 \), and \( y_2 = 4 \).
02

Calculate the Slope

Plug these values into the slope formula \( m = \frac{y_2-y_1}{x_2-x_1} \). Here, your m (slope) will be \( m = \frac{4-3}{2 - (-1)} = \frac{1}{3} \). Unlike a number divided by zero (which would be undefined), this calculation results in a defined slope of 1/3.
03

Determine the Rise or Fall

Since the slope is a positive number (1/3), it indicates that the line rises.

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Most popular questions from this chapter

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-6,4)\) and is perpendicular to the line that has an \(x\) -intercept of 2 and a \(y\) -intercept of \(-4\)

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((5,-9)\) and perpendicular to the line whose equation is \(x+7 y=12\)

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ for the given ordered pairs \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). $$\left(x_{1}, y_{1}\right)=(1,3) ;\left(x_{2}, y_{2}\right)=(6,13)$$

Solve for \(h: \quad V=\frac{1}{3} A h .\) (Section 2.4, Example 4)

Describe how to calculate the slope of a line passing through two points.
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