/*! 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 Find an equation of the line: w... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 35

Find an equation of the line: with slope \(0,\) containing \((2,3).\)

Short Answer

Expert verified
The equation of the line is \(y = 3\).

Step by step solution

01

Understand the Slope

The slope of a line represents its steepness. A slope of 0 means the line is horizontal.
02

Identify the Point

Given the point \((2, 3)\), we know the line passes through this point.
03

Write the Equation of a Horizontal Line

The equation of a horizontal line is always in the form of \(y = k\), where \(k\) is the y-coordinate of any point on the line. Since it passes through (2, 3), \(k=3\).
04

Final Equation

The equation of the line with a slope of 0 containing the point \((2, 3)\) is \(y = 3\).

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Key Concepts

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

Understanding Slope
The 'slope' of a line measures its steepness and direction. Imagine a slope as the angle at which a hill tilts. In mathematical terms, the slope is depicted as 'm' and calculated by how much 'y' changes for a change in 'x' between two points: \[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \]When the slope is 0, it means there is no vertical change as 'x' changes. This results in a flat, horizontal line.
Horizontal Line Explained
A horizontal line runs parallel to the x-axis, no matter how far it goes. This line鈥檚 equation is unique because it only depends on the y-coordinate. For example, a horizontal line that runs through the point \((2,3)\) is represented as: \[ y = k \]Here 'k' is the constant y-value at which this horizontal line passes. For the given point, this would be: \[ y = 3 \].
Point-Slope Form
The point-slope form is particularly handy for when you know a point on the line and the slope. It鈥檚 structured as: \[ y - y_1 = m(x - x_1) \]Where -\( (x_1, y_1) \) is a point on the line-\( m \) is the slopeIn our specific case, since the slope is 0, the formula simplifies. Plug in the point \((2, 3)\) and slope 0: \[ y - 3 = 0(x - 2) \] This simplifies to just: \[ y = 3 \], which is the equation of the line.

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Most popular questions from this chapter

Find the domain of each function given below. $$f(x)=\frac{2}{x+3}$$

Boxowitz, Inc., a computer firm, is planning to sell a new graphing calculator. For the first year, the fixed costs for setting up the new production line are 100,000 dollars. The variable costs for producing each calculator are estimated at 20 dollars. The sales department projects that 150,000 calculators can be sold during the first year at a price of 45 dollars each. a) Find and graph \(C(x),\) the total cost of producing \(x\) calculators. b) Using the same axes as in part (a), find and graph \(R(x),\) the total revenue from the sale of \(x\) calculators. c) Using the same axes as in part (a), find and graph \(P(x),\) the total profit from the production and sale of \(x\) calculators. d) What profit or loss will the firm realize if the expected sale of 150,000 calculators occurs? e) How many calculators must the firm sell in order to break even?

a) Graph \(x=y^{2}-3.\) b) Is this a function?

Consider the function \(\int\) given by $$f(x)=\left\\{\begin{array}{ll} -2 x+1, & \text { for } x<0 \\ 17, & \text { for } x=0 \\ x^{2}-3, & \text { for } 0

Use the vertical-line test to determine whether each graph is that of a function. (The vertical dashed lines are not part of the graph.)
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