9. graph \$y + 3 = -1\$

QUESTION IMAGE

$9. graph \$y + 3 = -1\$$

Question

graph \$y + 3 = -1\$

Explanation:

Response

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Isolate the variable y

To graph the equation, we first solve for $y$.
Subtract 3 from both sides:
\[y + 3 - 3 = -1 - 3\]
\[y = -4\]

Identify the line type

The equation $y = -4$ represents a horizontal line.
For any value of $x$, the $y$-coordinate is always $-4$.

Determine key points

We can choose any $x$-values to find points on this line.
For example:

If $x = -2$, then $y = -4$, giving point $(-2, -4)$.
If $x = 0$, then $y = -4$, giving point $(0, -4)$.
If $x = 2$, then $y = -4$, giving point $(2, -4)$.

Draw the horizontal line

Plot these points on the coordinate plane.
Connect them with a straight horizontal line passing through $-4$ on the $y$-axis.
</reasoning>

<answer>
The equation $y + 3 = -1$ simplifies to the horizontal line:
\[y = -4\]

To graph this line:

Locate $-4$ on the vertical $y$-axis.
Draw a straight, flat horizontal line passing through $(0, -4)$ that runs parallel to the $x$-axis.

</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-10, -4], [10, -4]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"name": "y = -4",
"withLabel": true,
"label": {
"position": "urt"
}
}
},
{
"type": "point",
"params": [[0, -4]],
"properties": {
"name": "(0, -4)",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
}
],
"timestamps": [0.5]
}
</plot>

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Answer: