Find the equation of a straight line passing through (−3,−1) having slope `-1/2`

Explanation

To find the equation of a straight line passing through the point \((-3, -1)\) with a slope of \(-\frac{1}{2}\), we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

### Step 1: Identify the values
Here, we have:
- \(x_1 = -3\)
- \(y_1 = -1\)
- \(m = -\frac{1}{2}\)

### Step 2: Substitute the values into the point-slope formula
Substituting these values into the point-slope form:

\[ y - (-1) = -\frac{1}{2}(x - (-3)) \]

This simplifies to:

\[ y + 1 = -\frac{1}{2}(x + 3) \]

### Step 3: Distribute the slope on the right side
Now, distribute \(-\frac{1}{2}\):

\[ y + 1 = -\frac{1}{2}x - \frac{3}{2} \]

### Step 4: Isolate \(y\)
Next, isolate \(y\) by subtracting \(1\) from both sides:

\[ y = -\frac{1}{2}x - \frac{3}{2} - 1 \]

### Step 5: Simplify the right side
Combine the constants on the right side:

\[ y = -\frac{1}{2}x - \frac{3}{2} - \frac{2}{2} \]
\[ y = -\frac{1}{2}x - \frac{5}{2} \]

### Step 6: Rearrange into standard form
To express this in standard form \(Ax + By + C = 0\), we can rearrange the equation:

\[ \frac{1}{2}x + y + \frac{5}{2} = 0 \]

To eliminate the fraction, multiply the entire equation by \(2\):

\[ x + 2y + 5 = 0 \]

Thus, the equation of the line is:

\[ x + 2y + 5 = 0 \]

### Summary
The required equation of the straight line passing through the point \((-3, -1)\) with a slope of \(-\frac{1}{2}\) is:

\[ x + 2y + 5 = 0 \]