/*! 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 35 Use the point on the line and th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 35

Use the point on the line and the slope \(m\) of the line to find three additional points through which the line passes. (There are many correct answers.)$$(2,1), \quad m=0$$

Short Answer

Expert verified
The three additional points through which the line passes are (1,1), (3,1), and (4,1).

Step by step solution

01

Understand the slope

The slope is zero, which means for every change in the x-coordinate, the y-coordinate stays constant because the rise (vertical change) over run (horizontal change) is zero. Therefore, all points on the line will have the y-coordinate as 1.
02

Select different x values

In order to find three additional points on the line, choose three different x-values. For simplicity, we'll choose 1, 3 and 4.
03

Determine the points

Keeping the y-coordinate constant at 1 (from our slope of zero), and using our chosen x values from step 2, we find the points to be (1,1), (3,1), and (4,1).

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.

Understanding Slope
The concept of slope is fundamental in coordinate geometry. It represents the steepness or incline of a line. Slope is often denoted by the letter \( m \) and is calculated as the "rise over run". In other words, it is the change in the y-values divided by the change in the x-values between two points on the line.
  • If the slope is positive, the line rises as you move from left to right.
  • If the slope is negative, the line falls as you move from left to right.
  • A zero slope means the line is horizontal; it doesn't rise or fall but runs parallel to the x-axis.
In the given exercise, the slope \( m \) is 0, indicating a horizontal line. This means no matter how far you move along the x-axis, the y-value remains constant.
What is a Horizontal Line?
A horizontal line in geometry is a straight line that runs left to right across the coordinate plane. It is defined by a constant y-value for all points on the line.
For example, in the equation \( y = c \), \( c \) is a constant, and the line is horizontal. In this case, the line will pass through all points with the y-coordinate equal to \( c \).
Since our exercise shows a slope of zero, our line is horizontal. Every point on our line has the same y-coordinate. Thus, for the exercise, given the point \((2, 1)\) and slope (m) of 0, every coordinate on the line will have a y-value of 1.
  • No matter the x-value you choose, the line's equation will be \( y = 1 \), forming a flat line.
  • The horizontal nature of the line simplifies finding additional points.
Finding Points on a Line
To find points on a line, especially a horizontal one, you begin by understanding the equation of the line, and in the case of a slope of 0, it remains unchanged: \( y = c \).
For our specific task, this equation becomes \( y = 1 \). Knowing this, you can select any x-value to generate a point on the line. This results in points that share a common y-value.
Let's explore this process:
  • Select any x-values. The choice could be anything you like; in this exercise, we used 1, 3, and 4.
  • By plugging these values into the equation \( y = 1 \), we found the corresponding points to be \((1,1)\), \((3,1)\), and \((4,1)\).
Finding additional points on a horizontal line is that simple. It can also be a great way to visualize the concept of slope as it solidifies understanding of different line types.

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

The lengths (in feet) of the winning men's discus throws in the Olympics from 1920 through 2008 are given by the following ordered pairs. $$\begin{aligned} &(1920,146.6) \quad(1956,184.9) \quad(1984,218.5)\\\ &(1924,151.3) \quad(1960,194.2) \quad(1988,225.8)\\\ &(1928,155.3) \quad(1964,200.1) \quad(1992,213.7)\\\ &(1932,162.3) \quad(1968,212.5) \quad(1996,227.7)\\\ &(1936,165.6) \quad(1972,211.3) \quad(2000,227.3)\\\ &\begin{array}{lll} (1948,173.2) & (1976,221.5) & (2004,229.3) \\ (1952,180.5) & (1980,218.7) & (2008,225.8) \end{array} \end{aligned}$$ (a) Sketch a scatter plot of the data. Let \(y\) represent the length of the winning discus throw (in feet) and let \(t=20\) represent 1920 (b) Use a straightedge to sketch the best-fitting line through the points and find an equation of the line. (c) Use the regression feature of a graphing utility to find the least squares regression line that fits the data. (d) Compare the linear model you found in part (b) with the linear model given by the graphing utility in part (c).

Write a sentence using the variation terminology of this section to describe the formula. Surface area of a sphere: \(S=4 \pi r^{2}\)

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(z\) varies directly as the square of \(x\) and inversely as \(y\) \((z=6 \text { when } x=6 \text { and } y=4 .)\)

The maximum load that can be safely supported by a horizontal beam varies jointly as the width of the beam and the square of its depth and inversely as the length of the beam. Determine the changes in the maximum safe load under the following conditions. (a) The width and length of the beam are doubled. (b) The width and depth of the beam are doubled.

Find a mathematical model for the verbal statement. The gravitational attraction \(F\) between two objects of masses \(m_{1}\) and \(m_{2}\) is jointly proportional to the masses and inversely proportional to the square of the distance \(r\) between the objects.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.