/*! 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 244 Find the slope of each line. \... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 244

Find the slope of each line. \(y=1\)

Short Answer

Expert verified
The slope of the line \(y=1\) is 0.

Step by step solution

01

Identify the Equation Format

The given equation is in the format of a horizontal line, where it is written as a constant value: \(y = c\).
02

Recognize the Slope of a Horizontal Line

In the equation \(y = 1\), the value of \(y\) does not change as the value of \(x\) changes. This means the line is horizontal.
03

Determine the Slope

For a horizontal line, the slope is always 0. Therefore, for \(y = 1\), the slope is \(m = 0\).

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Key Concepts

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

horizontal lines
Horizontal lines are lines that run parallel to the x-axis in a coordinate plane. In a horizontal line, the y-value remains constant for all x-values. This means that no matter what the x-value is, the y-value will always be the same. For example, in the equation \( y = 1 \), the y-value is always 1 regardless of the x-value.
  • Equation format: \(y = c\)
  • Y-value is constant
  • Parallel to the x-axis
Horizontal lines are easy to identify because they do not slant upward or downward; they travel straight across the plane level with the x-axis.
linear equations
Linear equations are equations of the first degree, which means their highest exponent is 1. They represent straight lines when plotted on a graph. The general form of a linear equation is \(Ax + By = C\), where A, B, and C are constants.
There are different forms of linear equations, but the slope-intercept form is commonly used:
\[y = mx + b\]
where:
  • \(m\) is the slope of the line
  • \(b\) is the y-intercept
Linear equations can represent different types of lines including vertical lines (\(x = c\)), horizontal lines (\(y = c\)), and slanted lines with a slope (\(m\)).
slope calculation
The slope of a line measures its steepness and direction and is represented by \(m\). The slope is calculated by the ratio of the change in y (rise) to the change in x (run). The formula to calculate the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
For horizontal lines, such as \(y = 1\), because the y-value remains constant, the change in y (rise) is 0. Therefore, the slope is always:
\[m = 0 / (x_2 - x_1) = 0\]
This shows that horizontal lines have a slope of 0, whereas vertical lines have an undefined slope as the run (change in x) would be 0.

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Most popular questions from this chapter

Graph the linear inequality \(y<-1\)

Find the equation of each line. Write the equation in slope-intercept form. Containing the points (-2,0) and (-3,-2)

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Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form. line \(y+7=0,\) point(1,-1)
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