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Chapter 5: Problem 6

Graph the equation. $$ y=5 $$

Short Answer

Expert verified
Answer: The graph of the equation y=5 is a horizontal line.

Step by step solution

01

Set up the coordinate system

Draw a coordinate system with x and y axes. Label the axes accordingly.
02

Locate y=5 on the y-axis

Find the point on the y-axis where y=5. This will be our reference point to draw the horizontal line.
03

Draw the horizontal line

Draw a horizontal line through the point (0,5) on the y-axis that extends indefinitely in both positive and negative x directions. This line represents every point where y is equal to 5, regardless of the value of x.
04

Label the line

Label the line "y = 5" to clearly indicate the equation it represents. The graph of the equation $$y=5$$ is a horizontal line passing through the point (0,5) on the y-axis and extending in both positive and negative x directions.

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Key Concepts

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

Coordinate System
A coordinate system is like a map for graphing equations. It includes two number lines that intersect at right angles. The vertical line is called the y-axis and the horizontal line is the x-axis. Their intersection point is the origin, designated as (0,0). This system allows us to locate any point in a plane using an ordered pair of numbers, known as coordinates.
  • The x-coordinate shows how far left or right the point is.
  • The y-coordinate tells us how far up or down the point is.
In our example, we use the coordinate system to plot the equation, which helps us visualize the line. By understanding this setup, graphing becomes much more intuitive.
Horizontal Line
A horizontal line is a straight line that runs from left to right across the graph. It has the same y-value for every point on the line. In our exercise, the equation is represented by a horizontal line. This is because y equals a constant value, in this case, y=5.
To graph a horizontal line:
  • Identify the y-value from the equation, which shows where to place the line on the y-axis.
  • Draw a straight line parallel to the x-axis, passing through this y-value.
Horizontal lines are simple to graph and are easily recognized because they do not slant up or down.
Equation Representation
Equations can be represented visually on a graph. This helps make relationships between variables easy to understand. When we talk about the equation y = 5, we mean that every point on the line has a y-coordinate of 5.
  • This equation doesn't depend on the x-coordinate.
  • All points (x, 5) will lie on the line, regardless of the value of x.
Labeling the line with its equation, 'y = 5', makes it clear which relationship you are graphing. Understanding this representation bridges the gap between algebraic equations and visual graphs.

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Most popular questions from this chapter

Without solving the equations, decide how many solutions the system has. $$ \left\\{\begin{array}{l} 4 x-3=y \\ \frac{4}{y}-\frac{1}{x}=\frac{3}{x y} \end{array}\right. $$

Solve the systems of equations in Problems \(34-41\). $$ \left\\{\begin{array}{l} 2 x+5 y=1 \\ 2 y-3 x=8 \end{array}\right. $$

Is the point-slope form or slopeintercept form the easier form to use when writing an equation for the line? Is parallel to the line \(y=0.4 x-5.5\) and has the same \(y\) -intercept as the line \(y=-2 x-3.4\)

Put the equation \(y=3 x t+2 x t^{2}+5\) in the form \(y=b+m x .\) What are the values of \(b\) and \(m ?\) [Note: Your answers could include \(t\).]

Which equation, (a)-(d), has the graph that crosses the \(y\) -axis at the highest point? (a) \(y=3(x-1)+5\) (b) \(x=3 y+2\) (c) \(y=1-6 x\) (d) \(2 y=3 x+1\)
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