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Chapter 1: Problem 72

Find the slope of each line described. A line parallel to \(y=5\)

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

Understand the given line equation

The given equation is in the form of a horizontal line: \(y=5\). This means that the y-coordinate is constant at 5 for all x-values.
02

Identify the slope of a horizontal line

For any horizontal line described by an equation of the form \(y=c\), where \(c\) is a constant, the slope is always 0 because there is no change in y as x changes.
03

Determine the slope of the parallel line

A line parallel to a horizontal line also has a slope of 0, because parallel lines have the same slope.

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Key Concepts

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

parallel lines
When you think about parallel lines, imagine two straight paths that never meet, no matter how far they extend. Both lines have the same slope, which means they rise and fall at the same rate if extended. If one line has a slope of 2, any line parallel to it will also have a slope of 2. This is a key concept because it helps us understand and predict the behavior of lines in different situations. Understanding parallel lines is particularly useful when working with geometric shapes and when solving problems involving navigation, engineering, and architecture.
horizontal lines
Horizontal lines are a special type of line where the slope is always zero. This is because they run left to right without any vertical change. If you look at the equation of a horizontal line, it will always be in the form of \(y = c\), where \(c\) is a constant. For example, the line \(y = 5\) is horizontal and crosses the y-axis at 5. No matter how much you change the x-value, the y-value remains at 5. Since there's no vertical change as we move along the line, the slope, which measures vertical change divided by horizontal change, is zero.
constant y-coordinate
The term 'constant y-coordinate' is used when describing horizontal lines. In a horizontal line, the y-value remains the same across all x-values. This means if you draw a horizontal line through the point (3,5), every point along this line will have 5 as the y-coordinate, whatever the x-coordinate is. Therefore, the equation of this line would be \(y = 5\). A constant y-coordinate simplifies many calculations in geometry and algebra, making it easier to understand and work with equations and graphs.

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Most popular questions from this chapter

Cost Accounting An accountant has been told to distribute a bonus to the employees that is \(15 \%\) of the company's net income. since the bonus is an expense to the accountant, it must be subtracted from the income to determine the net income. If the company has an income of \(\$ 140,000\) before the bonus, then the accountant must solve $$ B=0.15(140,000-B) $$ to find the bonus \(B\), Find \(B\).

Final Exam Score Lucky scored 65 points on his Psychology 101 midterm. If the average of his midterm and final must be between 79 and 90 inclusive for a \(B\), then for what range of scores on the final exam would Lucky get a B? Both tests have a maximum of 100 points. Write a compound inequality with his average between 79 and 90 inclusive.

Write a formula that expresses the diameter \(d\) of a circle as a function of its circumference \(C\).

Find the exact distance from each given point to the given line. $$(-2,5), y=-4 x+1$$

Find an exact solution to each problem. If the solution is irrational, then find an approximate solution also. Height of a Sky Diver A sky diver steps out of an airplane at 5000 ft. Use the formula \(S=-16 t^{2}+v_{0} t+s_{0}\) to find how long it takes the sky diver to reach \(4000 \mathrm{ft}\).
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