/*! 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 2 Describe the slant of a line wit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 2

Describe the slant of a line with a positive slope.

Short Answer

Expert verified
A line with a positive slope inclines upwards from left to right, indicating that its vertical position (y-value) increases as we move from left to right. The slope represents the steepness of this incline and can be calculated using the formula \(m = \frac{Rise}{Run}\), where larger positive values indicate a steeper incline.

Step by step solution

01

Understanding Slope

The slope of a line is a measure of its steepness or incline. It is represented by the letter 'm' and can be defined as the change in the vertical position (rise) divided by the change in the horizontal position (run) between any two points on the line. Mathematically, the slope can be expressed as: \(m = \frac{Rise}{Run}\).
02

Positive Slope

A positive slope indicates that the line inclines upwards from left to right. This means that as we move from left to right along the line, the line's vertical position (y-value) increases. In other words, the line rises as we move from left to right.
03

Graphical Representation

To visualize a positive slope, consider the following points on a two-dimensional plane: Point A (0, 0) and Point B (2, 1). The line segment connecting these two points has a positive slope because the y-value increases as we move from Point A to Point B. Here's how we can calculate the slope of this line segment: 1. Determine the difference in the y-values (rise), which is: \(1 - 0 = 1\) 2. Determine the difference in the x-values (run), which is: \(2 - 0 = 2\) 3. Calculate the slope, \(m = \frac{Rise}{Run} = \frac{1}{2}\) Since the calculated slope is a positive value (\(\frac{1}{2}\)), this line has a positive slope and rises from left to right.
04

Conclusion

A line with a positive slope describes an incline that rises from left to right. The slope value represents the steepness of this incline, with larger positive values indicating a steeper incline. The slope can be determined using the formula \(m = \frac{Rise}{Run}\).

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!

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

Write an equation of the line perpendicular to the given line and containing the given point. Write the answer in slope-intercept form or in standard form, as indicated. $$2 x+5 y=11 ;(4,2) ; \text { standard form }$$

Graph each function using the slope and \(y\) -intercept. $$f(x)=-x+5$$

Determine the domain of each relation, and determine whether each relation describes \(y\) as a function of \(x .\) $$y=\frac{2}{x-7}$$

Graph each function by making a table of values and plotting points. $$f(x)=x+2$$

Determine the domain of each relation, and determine whether each relation describes \(y\) as a function of \(x .\) $$y=\frac{1}{4 x}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Statistics

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.