The Table Represents A Linear Function.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -2 & -2 \\ \hline -1 & 1 \\ \hline 0 & 4 \\ \hline 1 & 7 \\ \hline 2 & 10 \\ \hline \end{tabular} \\]What Is The Slope Of The Function?A. -3 B.

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Introduction

In mathematics, a linear function is a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear function represents the rate of change of the function with respect to the input variable. In this article, we will explore how to find the slope of a linear function using a table of values.

What is a Linear Function?

A linear function is a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear function represents the rate of change of the function with respect to the input variable. In other words, it represents how much the output of the function changes when the input changes by one unit.

The Table of Values

The table of values represents a linear function. The table has two columns: x and y. The x column represents the input values, and the y column represents the corresponding output values.

x y
-2 -2
-1 1
0 4
1 7
2 10

Finding the Slope

To find the slope of the linear function, we need to calculate the rate of change of the function with respect to the input variable. We can do this by using the formula:

m = (y2 - y1) / (x2 - x1)

where m is the slope, and (x1, y1) and (x2, y2) are two points on the line.

Step 1: Choose Two Points

We need to choose two points on the line. Let's choose the points (-2, -2) and (2, 10).

Step 2: Calculate the Slope

Now, we can calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1) = (10 - (-2)) / (2 - (-2)) = (10 + 2) / (2 + 2) = 12 / 4 = 3

Conclusion

In this article, we explored how to find the slope of a linear function using a table of values. We used the formula m = (y2 - y1) / (x2 - x1) to calculate the slope of the function. We chose two points on the line, (-2, -2) and (2, 10), and calculated the slope using the formula. The slope of the function is 3.

The Final Answer

The final answer is 3\boxed{3}.

Discussion

The slope of a linear function represents the rate of change of the function with respect to the input variable. In this article, we used a table of values to find the slope of a linear function. We chose two points on the line and calculated the slope using the formula m = (y2 - y1) / (x2 - x1). The slope of the function is 3.

Related Topics

  • Linear functions
  • Slope of a linear function
  • Table of values
  • Rate of change

References

Keywords

  • Linear function
  • Slope
  • Table of values
  • Rate of change
  • Mathematics
    The Table Represents a Linear Function: Q&A =====================================================

Introduction

In our previous article, we explored how to find the slope of a linear function using a table of values. We used the formula m = (y2 - y1) / (x2 - x1) to calculate the slope of the function. In this article, we will answer some frequently asked questions related to linear functions and the table of values.

Q&A

Q: What is a linear function?

A: A linear function is a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

Q: What is the slope of a linear function?

A: The slope of a linear function represents the rate of change of the function with respect to the input variable.

Q: How do I find the slope of a linear function using a table of values?

A: To find the slope of a linear function using a table of values, you need to choose two points on the line and calculate the slope using the formula m = (y2 - y1) / (x2 - x1).

Q: What is the y-intercept of a linear function?

A: The y-intercept of a linear function is the point where the line intersects the y-axis. It is represented by the value of b in the equation y = mx + b.

Q: How do I determine if a function is linear or not?

A: To determine if a function is linear or not, you need to check if the function can be written in the form of y = mx + b. If it can, then the function is linear.

Q: What is the difference between a linear function and a non-linear function?

A: A linear function is a function that can be written in the form of y = mx + b, while a non-linear function is a function that cannot be written in this form.

Q: Can a linear function have a negative slope?

A: Yes, a linear function can have a negative slope. A negative slope means that the function is decreasing as the input variable increases.

Q: Can a linear function have a zero slope?

A: Yes, a linear function can have a zero slope. A zero slope means that the function is a horizontal line.

Q: Can a linear function have a positive slope?

A: Yes, a linear function can have a positive slope. A positive slope means that the function is increasing as the input variable increases.

Q: How do I graph a linear function?

A: To graph a linear function, you need to plot two points on the line and draw a line through them. You can also use the slope-intercept form of the equation to graph the function.

Q: What is the equation of a linear function in slope-intercept form?

A: The equation of a linear function in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I find the equation of a linear function given two points?

A: To find the equation of a linear function given two points, you need to calculate the slope using the formula m = (y2 - y1) / (x2 - x1) and then use the point-slope form of the equation to find the equation of the line.

Conclusion

In this article, we answered some frequently asked questions related to linear functions and the table of values. We hope that this article has been helpful in clarifying any doubts you may have had about linear functions.

The Final Answer

The final answer is 3\boxed{3}.

Discussion

The slope of a linear function represents the rate of change of the function with respect to the input variable. In this article, we used a table of values to find the slope of a linear function. We chose two points on the line and calculated the slope using the formula m = (y2 - y1) / (x2 - x1). The slope of the function is 3.

Related Topics

  • Linear functions
  • Slope of a linear function
  • Table of values
  • Rate of change

References

Keywords

  • Linear function
  • Slope
  • Table of values
  • Rate of change
  • Mathematics