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Chapter 11: Problem 192

In the following exercises, identify the most convenient method to graph each line. $$ y=-1 $$

Short Answer

Expert verified
Plot a horizontal line at y = -1.

Step by step solution

01

Identify the Type of Equation

The equation given is in the form of y = a constant. This represents a horizontal line.
02

Determine the Slope

For the equation y = -1, the slope of the line is 0. This means the line does not rise or fall but remains constant.
03

Find the Y-Intercept

The y-intercept of the equation y = -1 is -1. This means the line crosses the y-axis at the point (0, -1).
04

Plot the Line

To graph this line, plot the point (0, -1) on the graph and draw a straight horizontal line through this point extending in both directions.

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Key Concepts

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

Horizontal Lines
A horizontal line is one of the simplest types of lines you can graph. It is represented by an equation of the form y = c, where c is a constant. This means for any value of x, the value of y will always be c.

Imagine y = -1. No matter how much x changes, y is always -1. This makes horizontal lines very easy to graph.

To graph a horizontal line, just find the y-intercept, in this case (-1), and draw a straight line parallel to the x-axis at that point. You don't need to worry about the slope since it's always zero for horizontal lines.
Slope of a Line
The slope of a line measures how steep it is. It is often represented by the letter m. For a line given by the equation y = mx + b, m is the slope.

For horizontal lines like y = -1, the slope, m, is 0. This is because the line doesn鈥檛 rise or fall as it moves along the x-axis. It remains flat.

You can think of the slope as the 'tilt' of the line. If m is positive, the line rises from left to right. If m is negative, it falls. If m is zero, like in our example, the line is horizontal and completely flat.
Y-Intercept
The y-intercept is the point where the line crosses the y-axis. It is represented by the letter b in the slope-intercept form of a line, y = mx + b.

For the equation y = -1, the y-intercept is -1. This means the line crosses the y-axis at the point (0, -1).

When graphing, start by plotting the y-intercept. In this case, you plot the point (0, -1) on the graph. After that, draw a horizontal line through this point. This line extends infinitely in both directions along the x-axis. The y-intercept helps us determine exactly where the line sits on the graph.

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Most popular questions from this chapter

In the following exercises, for each ordered pair, decide a. if the ordered pair is a solution to the equation. b. if the point is on the line. \(y=\frac{2}{3} x-1\) (a) \((0,-1)\) (b) \((3,1)\) (c) \((-3,-3)\) (d) \((6,4)\)

In the following exercises, graph each pair of equations in the same rectangular coordinate system. $$ y=2 x \text { and } y=2 $$

In the following exercises, graph each equation. $$ 2 x+y=6 $$

In the following exercises, find three solutions to each linear equation. $$ y=-x-1 $$

In the following exercises, use the slope formula to find the slope of the line between each pair of points. $$ (3,5),(4,-1) $$
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