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Chapter 3: Problem 51

Graph each linear equation. $$ y=-1 $$

Short Answer

Expert verified
A horizontal line at y = -1.

Step by step solution

01

Understand the Equation

The given equation is a horizontal line. This means that for any value of x, the value of y will always be -1.
02

Identify Key Characteristics

Since the equation is y = -1, at any point on the graph, the y-coordinate will be -1. The x-coordinate can be any real number.
03

Plot Points

Choose a few values for x. For example: x = -2, x = 0, and x = 2. For each of these values of x, the value of y will remain -1. This gives you the points (-2, -1), (0, -1), and (2, -1).
04

Draw the Line

Plot the points on a graph and draw a straight horizontal line through them. This line is y = -1.

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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 unique because they have the same y-coordinate for every value of x. In the equation \( y = -1 \), no matter what x is, y will consistently be -1. This makes horizontal lines very predictable and easy to plot on a graph.

Horizontal lines are always parallel to the x-axis, which means they never intersect with it. This consistency is important when you're graphing because it ensures that the line will stay at a constant vertical position.
Plotting Points
Plotting points is an essential skill when it comes to graphing linear equations. To plot points, you need both x and y coordinates. For instance, let's take the equation \( y = -1 \):

1. Choose any value for x. It could be -2, 0, or 2 as examples.
2. Determine the corresponding y value, which in this case is always -1.
3. This gives you points like (-2, -1), (0, -1) and (2, -1).

Once you have these points, you can place them on your graph paper. Plot each point by finding the correct position for each x and y pair. It's similar to playing a game of connect-the-dots but with coordinates.
Coordinates on the Graph
Understanding coordinates is key when working with graphs. Coordinates are in the format (x, y), where x represents the horizontal position, and y represents the vertical position.

For example, coordinates like (-2, -1) mean that from the origin (0,0), you move 2 units to the left on the x-axis and 1 unit down on the y-axis.

Here鈥檚 a quick breakdown to make it clear:
  • The first number (x-coordinate) tells you how far to move horizontally.
  • The second number (y-coordinate) tells you how far to move vertically.
In the case of the equation \( y = -1 \) from our exercise, all plotted points will have different x-values, but y will always be -1.

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Most popular questions from this chapter

Find the \(x\) - and \(y\) -intercepts for the graph of each equation. $$ 5 x-2 y=20 $$

What is the common name given to a vertical line whose \(x\) -intercept is the origin?

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 2 x=4 y $$

Write an equation of the line satisfying the given conditions. Give the final answer in slope-intercept form. (Hint: Recall the relationships among slopes of parallel and perpendicular lines.) Perpendicular to \(x-2 y=7\) \(y\) -intercept (0,-3)

$$ y=\frac{x}{7}-\frac{5}{14} $$
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