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Chapter 5: Problem 74

Graph. $$y=-3$$

Short Answer

Expert verified
Graph a horizontal line at \ y = -3 \.

Step by step solution

01

Identify the Type of Equation

Recognize that the equation given is a horizontal line equation in the form of \(y = c\) where \(c\) is a constant.
02

Determine the Y-Coordinate

In the equation \(y = -3\), the constant \(c\) is \(-3\). This means that for every value of \(x\), the value of \(y\) will always be \(-3\).
03

Plot Points on the Graph

To graph this equation, select multiple values for \(x\). For example, choose \(x = -2, -1, 0, 1, 2\). For each value of \(x\), \(y\) will be \(-3\). Plot the points \((-2, -3), (-1, -3), (0, -3), (1, -3), (2, -3)\) on the graph.
04

Draw the Horizontal Line

Connect the points plotted in the previous step with a straight horizontal line. This line represents all points where \(y = -3\).
05

Label the Line

Label the line with the equation \(y = -3\) to indicate that all points on this line have a \(y\) value of \(-3\).

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Key Concepts

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

Equation of a Horizontal Line
A horizontal line in mathematics represents all points that have the same y-coordinate. The general form of the equation of a horizontal line is written as y = c, where c is a constant.
This simple form indicates that no matter what value x takes, y will always remain the same.
For example, in the equation given,
y = -3, the value of y is always -3, regardless of what x is.
This leads us to understand that all points lying on this line have a
y-coordinate of -3.
Plotting Points
To graph an equation, it's helpful to plot multiple points first.
This gives a visual representation of the equation on the graph.
In the context of a horizontal line like y = -3,
select various x-values to plot.
Let's say we choose x-values of
-2, -1, 0, 1, and 2. For each selected x-value,
the corresponding y-value will be -3 as derived from the equation.
  • The points to plot would be (-2, -3),
  • (-1, -3),
  • (0, -3),
  • (1, -3)
    • ,
  • and (2, -3).
Plot these points carefully on your graph paper or a digital tool
to form the foundation for the next step, drawing the line.
Graphing Linear Equations
Graphing linear equations helps us visually understand their behavior on a coordinate plane. For the equation y = -3, after choosing and plotting points from the previous step, we connect these points with a straight line.
Essentially forming a horizontal line. This line shows that y never changes, no matter the value of x.
Always point out the line with its equation:
y = -3. This labeling tells viewers that every point
on this line has a y value of -3.
Now we have a complete graph of the linear equation.
This process can be applied to graph other linear equations,
whether they are horizontal, vertical, or sloped lines.

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