/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 Find the slope of the line conta... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 52

Find the slope of the line containing each given pair of points. If the slope is undefined, state this. $$ (5,-2) \text { and }(-4,-2) $$

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

- Understand the Slope Formula

The slope of a line through two points \(x_1, y_1\) and \(x_2, y_2\) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \(m\) represents the slope.
02

- Identify the Coordinates

The given points are (5, -2) and (-4, -2). Assign the coordinates as follows: \((x_1, y_1) = (5, -2)\) and \((x_2, y_2) = (-4, -2)\).
03

- Substitute Values into the Formula

Substitute the coordinates into the slope formula: \[ m = \frac{-2 - (-2)}{-4 - 5} \]
04

- Simplify the Expression

Simplify the expression: \[ m = \frac{-2 + 2}{-4 - 5} = \frac{0}{-9} \]
05

- Interpret the Result

Since the numerator is 0 and the denominator is non-zero, the slope \(m\) is 0. This means the line is horizontal.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

coordinate geometry
Coordinate geometry, also known as analytic geometry, uses a coordinate system to define and represent geometric shapes. This system is essential in locating points on a plane and describing the relationships between them.
The fundamental elements in coordinate geometry include:
  • Points: Defined by coordinates \( (x, y) \), where \( x \) and \( y \) are numerical values representing the location on the horizontal and vertical axes, respectively.
  • Lines: Determined by the equation \[ y = mx + b \], where \( m \) represents the slope and \( b \) the y-intercept.
Understanding these basics allows us to explore more complex geometrical relationships and solve problems involving distances, midpoints, and slopes, as shown in this exercise.
slope formula
The slope formula is a key concept in coordinate geometry. It helps us determine the steepness or incline of a line between two points. The formula is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here's how it works:
  • \
horizontal line
A horizontal line is a special type of line in coordinate geometry. It runs parallel to the x-axis and has some unique characteristics:
  • Zero Slope: The slope of a horizontal line is always 0, as seen in our example. This is because there is no vertical change between any two points on the line.
  • Equation of the Line: The equation for a horizontal line can be written as \( y = c \), where \( c \) is a constant. For our exercise, the points (5, -2) and (-4, -2) lie on the line \( y = -2 \).
Recognizing horizontal lines is crucial, as they indicate that all points on the line have the same y-coordinate and no vertical movement.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Aerobic Exercise. The formula \(T=-\frac{3}{4} a+165\) can be used to determine the target heart rate, in number of beats per minute, for a person, \(a\) years old, participating in aerobic exercise. Graph the equation and interpret the significance of its slope.

To prepare for Section \(3.5,\) review subtraction and order of operations. Simplify. $$ \frac{5-(-4)}{-2-7} $$

Find the function values. $$f(x)=\frac{x-3}{2 x-5}$$ a) \(f(0)\) b) \(f(4)\) c) \(f(-1)\) d) \(f(3)\) e) \(f(x+2)\)

Suppose that a function \(g\) is such that \(g(-1)=-7\) and \(g(3)=8 .\) Find a formula for \(g\) if \(g(x)\) is of the form \(g(x)=m x+b,\) where \(m\) and \(b\) are constants.

Simplify. $$(-2)^{6}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.