Problem 115 Explain how you would choose thr... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 11: Problem 115

Explain how you would choose three $x$ -values to make a table to graph the line $y=\frac{1}{5} x-2$

Short Answer

Expert verified

Choose x-values like $-5$, $0$, and $5$, calculate corresponding y-values, and create a table with these pairs.

Step by step solution

- Understand the Equation

The given equation is $y = \frac{1}{5} x - 2$. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

- Select x-values

To create a table, choose three different and appropriate x-values. It is often useful to select evenly spaced values around zero for simplicity. For example, choose $-5$, $0$, and $5$.

- Calculate y-values

Substitute each chosen x-value into the equation to find the corresponding y-values. For $x = -5$, $y = \frac{1}{5}(-5) - 2 = -1 - 2 = -3$. For $x = 0$, $y = \frac{1}{5}(0) - 2 = -2$. For $x = 5$, $y = \frac{1}{5}(5) - 2 = 1 - 2 = -1$.

- Create the Table

Organize your results into a table. The x-values should be in one column and the corresponding y-values in another column. For example: \[\begin{array}{|c|c|} \hline x & y \ \hline -5 & -3 \ 0 & -2 \ 5 & -1 \ \hline\end{array} \]

- Graph the Points

Use the table to plot the points $(-5, -3)$, $(0, -2)$, and $(5, -1)$ on a coordinate plane. Connect the points with a straight line, as they represent a linear relationship.

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Key Concepts

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

Understanding the Slope-Intercept Form

The slope-intercept form of a linear equation is fundamental in graphing linear equations. The general equation is represented as:
First, we will identify the components in the equation.

The variable m represents the slope, indicating the steepness of the line. It tells us how much y changes for a unit change in x.
The variable b is the y-intercept, the point where the line crosses the y-axis.

In our exercise, the given equation is:
From the equation, we can see:

The slope m is $ \frac{1}{5} $.
The y-intercept b is -2.

This means the line will cross the y-axis at (0, -2) and rise 1 unit for every 5 units it moves to the right on the x-axis.

Selecting x-values Effectively

Choosing the right x-values is critical in plotting a linear equation accurately. In our case, we want to select values that make calculation simple and provide a broad view of the line.
Here are some tips for selecting x-values:

Choose evenly spaced x-values. This ensures the points are spread well, making the graph more accurate.
Include negative, zero, and positive values. This helps to visualize the line's behavior on both sides of the y-axis.

For our line $y = \frac{1}{5} x - 2$, choosing x = -5, x = 0, and x = 5 is effective. These values are evenly spaced and give us a good range to work with.
When we substitute these values into the equation, we get:

For x = -5: $y = \frac{1}{5}(-5) - 2 = -3$
For x = 0: $y = \frac{1}{5}(0) - 2 = -2$
For x = 5: $y = \frac{1}{5}(5) - 2 = -1$

This gives us the coordinates (-5, -3), (0, -2), and (5, -1).

Plotting on the Coordinate Plane

Now that we have our coordinates, it's time to plot them on a coordinate plane. Follow these simple steps:

Draw your x-axis (horizontal) and y-axis (vertical) on graph paper or use a graphing tool.
Label your axes with appropriate intervals to include all your points.

Start plotting the points one by one:

Mark (-5, -3) by moving 5 units left on the x-axis and 3 units down on the y-axis.
Mark (0, -2) at the intersection of the y-axis and 2 units down.
Mark (5, -1) by moving 5 units right on the x-axis and 1 unit down on the y-axis.

Connect the points with a straight line using a ruler. This straight line represents the graph of our equation $y = \frac{1}{5} x - 2$.
With these steps, you should have accurately graphed the linear equation. Remember, practice is key to mastering graphing linear equations!

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91影视

Explain how you would choose three \(x\) -values to make a table to graph the line \(y=\frac{1}{5} x-2\)

Short Answer

Step by step solution

- Understand the Equation

- Select x-values

- Calculate y-values

- Create the Table

- Graph the Points

Key Concepts

Understanding the Slope-Intercept Form

Selecting x-values Effectively

Plotting on the Coordinate Plane

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