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To solve the problem, we need to find the point-slope form of a line given the slope and a point through which the line passes.

### Given:
- **Slope (m) = -4**
- **Point (x₁, y₁) = (-3, -5/2)**

### Step 1: Write the Point-Slope Form
The point-slope form of the equation of a line is:

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

Plugging in the given values:

\[
y - \left(-\frac{5}{2}\right) = -4(x - (-3))
\]

This simplifies to:

\[
y + \frac{5}{2} = -4(x + 3)
\]

### Step 2: Convert to Slope-Intercept Form
Now, distribute and simplify to find the slope-intercept form:

\[
y + \frac{5}{2} = -4x - 12
\]

Subtract \(\frac{5}{2}\) from both sides:

\[
y = -4x - 12 - \frac{5}{2}
\]

Convert \(-12\) to a fraction with a denominator of 2:

\[
y = -4x - \frac{24}{2} - \frac{5}{2}
\]

Combine like terms:

\[
y = -4x - \frac{29}{2}
\]

### Final Answer:
- **Point-Slope Form:** \(y + \frac{5}{2} = -4(x + 3)\)
- **Slope-Intercept Form:** \(y = -4x - \frac{29}{2}\)

Would you like any more details or have any questions?

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Here are 5 related questions to expand on the topic:
1. How do you convert a point-slope form to a standard form?
2. What is the geometric interpretation of the slope in a linear equation?
3. How would the equation change if the slope were positive?
4. Can you find the x- and y-intercepts from the slope-intercept form?
5. How would you graph the line given its slope and a point?

**Tip:** Always double-check your calculations when converting between different forms of linear equations to avoid simple errors!

Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope = -4, passing through (-3, -5/2).

Learn how to write the point-slope form and convert it to the slope-intercept form for a line with slope -4 passing through the point (-3, -5/2). Suitable for students in Grades 9-12, covering linear equations and graphing concepts.

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