Answered

IDNLearn.com connects you with experts who provide accurate and reliable answers. Join our community to receive prompt and reliable responses to your questions from experienced professionals.

Complete the equation describing how [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are related.

[tex]\[
\begin{array}{c|c}
x & y \\
\hline
-3 & -39 \\
-2 & -29 \\
-1 & -19 \\
0 & -9 \\
1 & 1 \\
2 & 11 \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To determine the linear relationship [tex]\(y = mx + c\)[/tex] between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from the provided table, we follow these steps:

1. Plot the Points:
Let's plot the given points [tex]\((-3, -39)\)[/tex], [tex]\((-2, -29)\)[/tex], [tex]\((-1, -19)\)[/tex], [tex]\((0, -9)\)[/tex], [tex]\((1, 1)\)[/tex], and [tex]\((2, 11)\)[/tex] on the Cartesian plane.

2. Determine the Slope (m):
The slope [tex]\(m\)[/tex] of the linear equation [tex]\(y = mx + c\)[/tex] represents the steepness of the line. It can be calculated from the given points.

The slope [tex]\(m\)[/tex] is calculated as follows:
[tex]\[ m = \frac{\Delta y}{\Delta x} \][/tex]
Where [tex]\(\Delta y\)[/tex] is the change in [tex]\(y\)[/tex] values and [tex]\(\Delta x\)[/tex] is the change in [tex]\(x\)[/tex] values.

3. Calculate the Y-Intercept (c):
The y-intercept [tex]\(c\)[/tex] is the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex].

Once computed, the linear equation [tex]\(y = mx + c\)[/tex] will describe the relation between [tex]\(x\)[/tex] and [tex]\(y\)[/tex].

From the table:

- When [tex]\(x = -3\)[/tex], [tex]\(y = -39\)[/tex]
- When [tex]\(x = -2\)[/tex], [tex]\(y = -29\)[/tex]
- When [tex]\(x = -1\)[/tex], [tex]\(y = -19\)[/tex]
- When [tex]\(x = 0\)[/tex], [tex]\(y = -9\)[/tex]
- When [tex]\(x = 1\)[/tex], [tex]\(y = 1\)[/tex]
- When [tex]\(x = 2\)[/tex], [tex]\(y = 11\)[/tex]

Upon calculating, we find:

- The slope [tex]\(m \approx 10.0\)[/tex]
- The y-intercept [tex]\(c \approx -9.0\)[/tex]

Thus, the linear equation describing the relationship is:
[tex]\[ y = 10x - 9 \][/tex]

To confirm, this means that for each unit increase in [tex]\(x\)[/tex], [tex]\(y\)[/tex] increases by approximately 10 units, and when [tex]\(x = 0\)[/tex], [tex]\(y \approx -9\)[/tex]. This relationship accurately fits the given data points. The polynomial equation in the standard form is:

[tex]\[ y = 10x - 9 \][/tex]

Therefore, the completed equation describing the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from the data provided is:

[tex]\[ y = 10x - 9 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.