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Chapter 3: Problem 52

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

Short Answer

Expert verified
The slope of a line passing through two points can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are points on the line.

Step by step solution

01

Identify the Points

Firstly, identify two points on the line, let's denote them as \( (x_1, y_1) \) and \( (x_2, y_2) \).
02

Understand the Slope Formula

Understand that the formula to calculate the slope \( m \) between these two points is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
03

Apply the Slope Formula

Finally, substitute the coordinates of \( (x_1, y_1) \) and \( (x_2, y_2) \) into the formula and calculate the slope.

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Most popular questions from this chapter

If you are given an equation of the form \(A x+B y=C\) explain how to find the \(y\)-intercept.

Find the absolute value: \(|-13.4|\)

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \leq 4 x+4$$

a. Graph each of the following points: $$ \left(1, \frac{1}{2}\right),(2,1),\left(3, \frac{3}{2}\right),(4,2) $$ Parts (b)-(d) can be answered by changing the sign of one or both coordinates of the points in part (a). b. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(y\) -axis of your graph in part (a)? c. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(x\) -axis of your graph in part (a)? d. What must be done to the coordinates so that the resulting graph is a straight-line extension of your graph in part (a)?

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{1}{2} x$$
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