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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 \(m\).

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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.

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Most popular questions from this chapter

Write the equation in the form \(y=m x+b\). $$6 x-5 y=10$$

Explain how you would distinguish between the graphs of the two equations. a. \(y=\frac{3}{4} x+5\) b. \(y=\frac{3}{4} x-5\)

What effect does increasing the constant term have on the graph of \(y=m x+b ?\)

In which quadrant is the graph of \((2,-5)\) located?

Find the \(x\) - and \(y\) -intercepts. $$5 x-y=-10$$
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