Problem 112 In the following exercises, grap... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 11: Problem 112

In the following exercises, graph each equation. $$ x=-4 $$

Short Answer

Expert verified

Graph a vertical line at x = -4.

Step by step solution

Understand the equation

The equation given is simple: it states that the value of the variable x is always -4.

Identify the kind of line

Since the equation is in the form of x = constant, it represents a vertical line.

Identify the position of the line

The line will be located at x = -4 for any value of y.

Plot points on the graph

Plot several points where x = -4. For example, (-4, 0), (-4, 1), (-4, -1), etc.

Draw the line

Connect the plotted points with a straight vertical line to complete the graph.

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Key Concepts

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

vertical lines

A vertical line on a graph is one where the value of x is constant. This means wherever you go on this line, x doesn't change. In our example, the equation is x = -4. This implies that all points along this line have an x-coordinate of -4. When graphing a vertical line, one key indicator is that the formula will be in the format of x = constant. It's essential to note that no matter what the y value is, x remains fixed. Thus, the line is perfectly vertical.

plotting points

Plotting points is a fundamental skill in graphing. Points are represented as (x, y) coordinates. For example, in this exercise, we're given x = -4. We need to create several points to draw a line. Start by choosing a few y-values. Suppose we pick y = 0, 1, and -1. This results in the points (-4, 0), (-4, 1), and (-4, -1). To plot these points on a graph, find -4 on the x-axis and draw a small dot where it intersects with the respective y-values. This gives us the plotted points needed to form our line.

axis identification

Knowing your axes is crucial for plotting. The x-axis runs horizontally, representing the value of x. The y-axis runs vertically, carrying the value of y. For the equation x = -4, we start by locating -4 on the x-axis. Then, we mark points directly above and below -4, which intersect with the y-axis. These intersections help us to form our vertical line. Properly identifying and understanding the axes allow precise plotting and accurate representation of equations on a graph.

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91影视

In the following exercises, graph each equation. $$ x=-4 $$

Short Answer

Step by step solution

Understand the equation

Identify the kind of line

Identify the position of the line

Plot points on the graph

Draw the line

Key Concepts

vertical lines

plotting points

axis identification

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