/*! 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 1 What is the symbol for slope in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 1

What is the symbol for slope in the equation \(y=m x+b ?\)

Short Answer

Expert verified
The symbol for slope in the equation \(y = m x + b\) is \(m\).

Step by step solution

01

Understanding the linear equation in slope-intercept form

In the slope-intercept form of a linear equation, \(y = mx + b\), \(y\) and \(x\) are variables representing the coordinates on a line, \(b\) is the y-intercept (where the line crosses the y-axis), and \(m\) represents the slope of the line.
02

Identify the symbol for slope

As explained in step 1, in the equation \(y = mx+b\), the slope of the line is represented by the symbol \(m\).

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.

Linear Equation
A linear equation is a mathematical statement that shows a linear relationship between two variables, usually represented as \(x\) and \(y\). The equation forms a straight line when graphed on a coordinate plane.
Linear equations are fundamental in algebra and can be written in various forms, but the slope-intercept form is one of the most commonly used.
A linear equation can be expressed in the general form \(ax + by + c = 0\), where \(a\), \(b\), and \(c\) are constants.
  • The equation portrays a consistent rate of change between the two variables.
  • This kind of equation helps to determine the value of one variable given the value of the other.
Recognizing a linear equation is essential for understanding the pattern and behavior of straight-line graphs.
Slope-Intercept Form
The slope-intercept form is a straightforward way to express linear equations and is written as \(y = mx + b\). This form is incredibly handy in quickly identifying key attributes of a linear graph.
Here, \(m\) represents the slope, while \(b\) is the y-intercept. Using this form helps uncover the characteristics of a line easily without needing to rearrange the equation.
  • The slope \(m\) signifies the line's steepness and direction.
  • The y-intercept \(b\) is where the line crosses the y-axis.
Using slope-intercept form allows for an easy transition from an equation to a graph.
Y-Intercept
In the equation \(y = mx + b\), the term \(b\) represents the y-intercept.
The y-intercept is the point where the line crosses the y-axis, which means \(x = 0\) at this location.
  • It is a critical point that can help in graphing the linear equation accurately.
  • The y-intercept provides a starting point for drawing the line on a graph.
Knowing the y-intercept allows you to envision how the line will pass through the coordinate plane, even if you only have the equation at hand.

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

Suppose \(A\) is a negative number, and \(B\) and \(C\) are positive numbers. Does the \(y\) -intercept of the graph of \(A x+B y=C\) lie above or below the \(x\) -axis? Does the graph slant upward to the right or downward to the right?

Evaluate a function. Given \(f(x)=x^{2},\) find \(f(3)\).

Graph by using the slope and \(y\) -intercept. (GRAPH CAN'T COPY) $$5 x-2 y=10$$

Find the domain and range of the relation. State whether or not the relation is a function. $$\\{(2,2),(2,4),(2,6),(2,8)\\}$$

Does \(y=2 x+3,\) where \(x \in\\{-2,-1,1,4\\},\) define \(y\) as a function of \(x ?\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.