Possible Table Representation

Oct 13, 2025 by talynt.org 139 views

Introduction

Ava's expression $\frac{4-2}{3-1}$ is used to determine the slope of a line. The slope of a line is a measure of how steep it is and can be calculated using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. In this case, Ava has used the points $(3, 1)$ and $(4, 2)$ to calculate the slope.

Calculating the Slope

To calculate the slope, we can use the formula $\frac{y_2 - y_1}{x_2 - x_1}$ . Plugging in the values, we get:

\frac{2 - 1}{4 - 3} = \frac{1}{1} = 1

So, the slope of the line is 1.

Possible Table Representation

Now that we have the slope, we need to find a table that represents Ava's line. A table that represents a line is a table where the values of $x$ and $y$ are related by a linear equation. In this case, we can use the slope-intercept form of a linear equation, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Slope-Intercept Form

Since the slope is 1, we can write the equation of the line in slope-intercept form as:

y = x + b

To find the value of $b$ , we can use one of the points on the line. Let's use the point $(3, 1)$ .

1 = 3 + b

Solving for $b$ , we get:

b = -2

So, the equation of the line is:

y = x - 2

Possible Table Representation

Now that we have the equation of the line, we can create a table that represents Ava's line. Here is one possible table:

$x$	$y$
1	-1
2	0
3	1
4	2

This table represents the line $y = x - 2$ .

Conclusion

In conclusion, Ava's expression $\frac{4-2}{3-1}$ is used to determine the slope of a line. The slope of the line is 1, and the equation of the line is $y = x - 2$ . A possible table that represents Ava's line is the one shown above.

Discussion

The table shown above represents a line with a slope of 1 and a y-intercept of -2. This line passes through the points $(1, -1)$ , $(2, 0)$ , $(3, 1)$ , and $(4, 2)$ . The line has a positive slope, which means that it rises from left to right.

Possible Alternative Tables

There are many possible tables that represent Ava's line. Here are a few alternative tables:

$x$	$y$
2	1
3	2
4	3
5	4

This table represents the line $y = x - 1$ .

$x$	$y$
1	0
2	1
3	2
4	3

This table represents the line $y = x$ .

$x$	$y$
3	0
4	1
5	2
6	3

This table represents the line $y = x - 3$ .

Conclusion

Introduction

In our previous article, we explored Ava's expression $\frac{4-2}{3-1}$ and how it can be used to determine the slope of a line. We also created a table that represents Ava's line. In this article, we will answer some frequently asked questions about Ava's line.

Q: What is the slope of Ava's line?

A: The slope of Ava's line is 1.

Q: What is the equation of Ava's line?

A: The equation of Ava's line is $y = x - 2$ .

Q: What is the y-intercept of Ava's line?

A: The y-intercept of Ava's line is -2.

Q: What are some points on Ava's line?

A: Some points on Ava's line are $(1, -1)$ , $(2, 0)$ , $(3, 1)$ , and $(4, 2)$ .

Q: Is Ava's line a horizontal line?

A: No, Ava's line is not a horizontal line. It has a positive slope, which means that it rises from left to right.

Q: Is Ava's line a vertical line?

A: No, Ava's line is not a vertical line. It has a non-zero slope, which means that it is not a vertical line.

Q: Can I create a table that represents Ava's line?

A: Yes, you can create a table that represents Ava's line. Here is one possible table:

$x$	$y$
1	-1
2	0
3	1
4	2

Q: Can I create a table that represents a different line?

A: Yes, you can create a table that represents a different line. For example, you can create a table that represents the line $y = x + 2$ .

$x$	$y$
1	3
2	4
3	5
4	6

Q: How do I know if a table represents a line?

A: To determine if a table represents a line, you can check if the values of $x$ and $y$ are related by a linear equation. If they are, then the table represents a line.

Q: Can I use Ava's expression to determine the slope of a different line?

A: Yes, you can use Ava's expression to determine the slope of a different line. However, you will need to use different points on the line to calculate the slope.

Conclusion

Discussion

Possible Alternative Tables

There are many possible tables that represent Ava's line. Here are a few alternative tables:

$x$	$y$
2	1
3	2
4	3
5	4

This table represents the line $y = x - 1$ .

$x$	$y$
1	0
2	1
3	2
4	3

This table represents the line $y = x$ .

$x$	$y$
3	0
4	1
5	2
6	3

This table represents the line $y = x - 3$ .