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Chapter 3: Problem 48

Graph each linear equation. \(y=3\)

Short Answer

Expert verified
A horizontal line at y=3.

Step by step solution

01

Identify the type of equation

The equation is in the form of a horizontal line because there is no variable for x, and y is equal to a constant value.
02

Determine the y-value

In the given equation, y is equal to 3. This means that for every x-value, the y-value will always be 3.
03

Plot points on the graph

Since y = 3 for any value of x, plot several points where y is 3. For example, plot points (0, 3), (1, 3), (2, 3), etc.
04

Draw the line

Draw a straight horizontal line through all the plotted points. The line will be parallel to the x-axis, passing through y = 3.

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Key Concepts

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

horizontal line
A horizontal line in a graph represents all the points where the y-value remains constant, no matter what the x-value is. This means the line runs parallel to the x-axis. In our example problem, the equation is given as \(y=3\). This tells us that the y-value is fixed at 3 for any value of x. To put it simply, if you imagine walking along this line, you'll stay level, always at the same height above the x-axis.
constant y-value
The concept of a constant y-value means that in the equation \(y=3\), the y-coordinate does not change regardless of any changes in the x-coordinate. Whether you pick \(x=0\), \(x=10\), or even \(x=-5\), the y-value will always be 3. This constant y-value creates a horizontal line on the graph. It's a simple, but powerful concept that helps in graphing linear equations quickly.
plotting points
Plotting points for a horizontal line involves finding coordinates where the y-value is always the same. For the equation \(y=3\), you pick various x-values and pair them with 3. For example:
  • (0, 3)
  • (1, 3)
  • (-2, 3)
Once you have these points plotted, draw a straight line through them. This line will be parallel to the x-axis, clearly showing that the y-value does not change. Practice with more points and see the pattern; all points will align horizontally at y=3.

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Most popular questions from this chapter

For each pair of equations, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither. See Example \(6 .\) $$ \begin{aligned} 5 x-y &=1 \\ x-5 y &=-10 \end{aligned} $$

Graph each linear equation. \(x=-y+6\)

\(\mathrm{Do}(4,-1)\) and \((-1,4)\) represent the same ordered pair? Explain.

Graph each linear equation. \(x-y=4\)

Graph each linear equation. \(y=-6 x\)
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