Question

respond to the following based on your reading.

1. complete the table of values below and use it to graph the equation \\(y - x = -6\\).

\\(\

$$\begin{array}{c|c|c|c} x & 1 & 2 & 3 \\\\ \\hline y & & & \\end{array}$$

\\)

1. find the slope of the line below.

Explanation:

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<reasoning>

Solve for y-values in the table

Using the equation \(y - x = -6\), solve for \(y\) by rewriting it as \(y = x - 6\):
\[

$$\begin{aligned} &\text{For } x = 1: \quad y = 1 - 6 = -5\\ &\text{For } x = 2: \quad y = 2 - 6 = -4\\ &\text{For } x = 3: \quad y = 3 - 6 = -3 \end{aligned}$$

\]

Find the slope of the line in Question 2

Identify two points on the given line from the graph: \((0, 5)\) and \((2, -1)\). Apply the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
\[
m = \frac{-1 - 5}{2 - 0} = \frac{-6}{2} = -3
\]
</reasoning>

<answer>

Question 1

\(x\)	1	2	3

Question 2

The slope of the line is \(-3\).
</answer>

<plot>
{
"elements": [
{
"type": "functiongraph",
"params": [
{
"js": "x - 6",
"latex": "x - 6"
},
-10,
10
],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"name": "y - x = -6",
"withLabel": true
}
},
{
"type": "point",
"params": [[1, -5]],
"properties": {
"name": "(1, -5)",
"color": "#5583F2",
"size": 3
}
},
{
"type": "point",
"params": [[2, -4]],
"properties": {
"name": "(2, -4)",
"color": "#5583F2",
"size": 3
}
},
{
"type": "point",
"params": [[3, -3]],
"properties": {
"name": "(3, -3)",
"color": "#5583F2",
"size": 3
}
},
{
"type": "functiongraph",
"params": [
{
"js": "-3*x + 5",
"latex": "-3x + 5"
},
-10,
10
],
"properties": {
"strokeColor": "#F2557F",
"strokeWidth": 2,
"name": "Line from Q2",
"withLabel": true
}
}
]
}
</plot>

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Answer:

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<reasoning>

Solve for y-values in the table

Using the equation \(y - x = -6\), solve for \(y\) by rewriting it as \(y = x - 6\):
\[

$$\begin{aligned} &\text{For } x = 1: \quad y = 1 - 6 = -5\\ &\text{For } x = 2: \quad y = 2 - 6 = -4\\ &\text{For } x = 3: \quad y = 3 - 6 = -3 \end{aligned}$$

\]

Find the slope of the line in Question 2

Identify two points on the given line from the graph: \((0, 5)\) and \((2, -1)\). Apply the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
\[
m = \frac{-1 - 5}{2 - 0} = \frac{-6}{2} = -3
\]
</reasoning>

<answer>

Question 1

\(x\)	1	2	3

Question 2

The slope of the line is \(-3\).
</answer>

<plot>
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"elements": [
{
"type": "functiongraph",
"params": [
{
"js": "x - 6",
"latex": "x - 6"
},
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10
],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"name": "y - x = -6",
"withLabel": true
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"params": [[2, -4]],
"properties": {
"name": "(2, -4)",
"color": "#5583F2",
"size": 3
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},
{
"type": "point",
"params": [[3, -3]],
"properties": {
"name": "(3, -3)",
"color": "#5583F2",
"size": 3
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"params": [
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"js": "-3*x + 5",
"latex": "-3x + 5"
},
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10
],
"properties": {
"strokeColor": "#F2557F",
"strokeWidth": 2,
"name": "Line from Q2",
"withLabel": true
}
}
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}
</plot>

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