/*! 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 40 Determine the slope and y-interc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 40

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$y=12$$

Short Answer

Expert verified
The slope of the given equation is 0 and the y-intercept is 12. The graph of the equation is a horizontal line parallel to x-axis that intersects the y-axis at the point (0,12).

Step by step solution

01

Determine the Slope

For the equation of the form \(y=b\), where \(b\) is a constant, the slope is always 0. So, the slope of the given equation \(y=12\) is 0.
02

Determine the y-intercept

For the equation of the form \(y=b\), where \(b\) is a constant, the y-intercept is the value of \(b\). So, the y-intercept of the equation \(y=12\) is 12.
03

Describe the Graph

The graph of the equation \(y=12\) is a horizontal line parallel to x-axis that intersects the y-axis at the point (0,12). Since the slope is 0, there's no inclination and the line remains flat, parallel to the x-axis.

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
In the world of linear equations, the slope is a key concept that describes the direction and steepness of a line. Simply put, the slope tells us how much the line rises or falls as it moves horizontally across the graph. For any equation in the form \(y = b\), such as our equation \(y=12\), the slope is 0. This is because as you move along the line, the y-value does not change鈥攊t remains constant at 12, no matter the x-value. A slope of 0 indicates that the line is completely horizontal. This means it does not ascend or descend at all, staying perfectly flat across the graph.
Identifying the Y-Intercept
The y-intercept is the point where the line crosses the y-axis. In linear equations, it's expressed as \(b\) in the form \(y = mx + b\). But when it comes to equations like \(y = 12\), where there is no \(m\) or \(x\), the concept simplifies. The given constant, 12, directly tells us the y-intercept. Hence, for \(y = 12\), the line intercepts the y-axis at 12. This means that when \(x\) is 0, \(y\) is 12, giving us the exact point of intersection at (0, 12).
What is a Horizontal Line?
A horizontal line is characterized by having a slope of 0. This type of line runs parallel to the x-axis.
Horizontal lines like \(y = 12\) have unique features:
  • They do not rise or fall, ensuring that the y-value remains consistent across all x-values.
  • The equation is independent of x, meaning no matter what value x takes, y will always be 12.
  • Such lines are always flat, with no tilt towards the x-axis.
In real-world scenarios, horizontal lines can represent situations where a specific condition remains constant, such as a flat rate or a fixed salary.
Describing the Graph
Graphically interpreting the equation \(y = 12\) provides a clear visual representation that is easy to understand. Upon plotting the equation, the line appears horizontally and traverses from left to right, never changing its y-value of 12. Here's how we can describe this graph:
  • The line runs parallel to the x-axis, illustrating it is horizontal.
  • It intersects the y-axis precisely at the point (0, 12), corresponding to the y-intercept.
  • Due to the zero slope, the line lacks any inclination or decline.
This comprehensive description makes it evident that the equation results in a graph where, no matter the x-value, the y-value steadfastly remains 12, embodying a perfect horizontal line that maintains its steadiness across the graph.

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

Use the functions \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$(g \circ f)^{-1}$$

Think About It The function \(f(x)=\frac{9}{5} x+32\) can be used to convert a temperature of \(x\) degrees Celsius to its corresponding temperature in degrees Fahrenheit. (a) Using the expression for \(f,\) make a conceptual argument to show that \(f\) has an inverse function. (b) What does \(f^{-1}(50)\) represent?

Determine whether the lines \(L_{1}\) and \(L_{2}\) passing through the pairs of points are parallel, perpendicular, or neither.$$\begin{aligned}&L_{1}:(-1,-7),(4,3)\\\&L_{2}:(1,5),(-2,-7)\end{aligned}$$.

Prove that a function of the following form is even. $$y=a_{2 n} x^{2 n}+a_{2 n-2} x^{2 n-2}+\cdots+a_{2} x^{2}+a_{0}$$

Find the domain of the function.$$f(x)=\frac{4}{9-x}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.