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Chapter 5: Problem 40

Determine the slope of the line from its equation. $$y=-4 x+2$$

Short Answer

Expert verified
The slope is -4.

Step by step solution

01

Identify the Equation Form

Recognize that the given equation is in the slope-intercept form which is written as: \[y = mx + b\] where \(m\) represents the slope and \(b\) represents the y-intercept.
02

Extract the Slope

In the given equation, \(y = -4x + 2\), compare it to the slope-intercept form equation \(y = mx + b\). The coefficient of \(x\) is \(-4\), so the slope \(m\) is \(-4\).

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Key Concepts

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

slope-intercept form
When dealing with linear equations, the slope-intercept form is one of the most common and useful formats you'll encounter. The slope-intercept form is expressed as y = mx + b.
  • y - The dependent variable (usually represents something you're trying to predict or measure).
  • x - The independent variable (usually represents the input or cause).
  • m - The slope of the line, which tells you how steep the line is and the rate at which y changes for a change in x.
  • b - The y-intercept, where the line crosses the y-axis (vertical axis).
Understanding this form can make solving or graphing linear equations much simpler.
linear equations
Linear equations represent straight lines when plotted on a graph. These equations have the general form of y = mx + b.These lines are characterized by having a constant slope, meaning the rate of change between the two variables is steady.
  • They can be written in different forms, such as slope-intercept form (y = mx + b) or standard form (Ax + By = C).
  • They are fundamental in understanding relationships in algebra, as many real-world scenarios can be modeled with linear equations.
When you understand that each term in a linear equation plays a specific role, it becomes easier to interpret and manipulate the equation.
extracting the slope
Extracting the slope from an equation in the slope-intercept form is straightforward. Recall our generic slope-intercept form y = mx + b.To find the slope (m), you focus on the coefficient of x.
  • Identify the term next to x. This coefficient represents the slope.
  • In the equation y = -4x + 2, the term next to x is -4.
  • Thus, the slope (m) in this equation is -4.
Always remember, the slope conveys how steep the line is and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

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Most popular questions from this chapter

Write an equation of the line satisfying the given conditions. Horizontal line passing through \((2,3)\)

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