Question

In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example $5 .$ $$ (a, b) \text { and }(c, d) \quad(a \neq c) $$

Name: Problem 53, Chapter 1: Finite Mathematics and Applied Calculus
Uploaded: 2021-09-03T16:14:41-08:00
Duration: 1 min 2 s
Channel: Tyler Moulton
Description: In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example 5 . (a, b) and (c, d) (a ≠c)

   In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example $5 .$
$$ (a, b) \text { and }(c, d) \quad(a \neq c) $$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 7th Edition

Chapter 1, Problem 53

Instant Answer

Solved by Expert Tyler Moulton

09/03/2021

Step 1

The formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where $ (x_1, y_1) $ and $ (x_2, y_2) $ are the coordinates of the two points. Show more…

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In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example $5 .$ $$ (a, b) \text { and }(c, d) \quad(a \neq c) $$

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Key Concepts

Slope

The slope of a line is a measure of its steepness and direction. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Exact Slope Calculation

Calculating the exact slope involves using the formula (d - b) / (c - a) for two points (a, b) and (c, d) on the line and simplifying the resulting fraction to its simplest form. This avoids decimal approximations and provides an exact value.

Undefined Slope

A slope is undefined when the horizontal distance between the two points is zero (i.e., when a = c). This occurs because division by zero is not defined in mathematics, which corresponds to the case of a vertical line.

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