Question

1. graph \\(y + 3 = -1\\)

Explanation:

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.

Answer:

The equation \(y + 3 = -1\) simplifies to the horizontal line:

$$y = -4$$

To graph this line:

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