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The uploaded image contains a series of math problems related to writing equations of lines, identifying slopes, and solving word problems. I will analyze the contents and solve the problems provided.

### Problem 1:
**Write an equation in point-slope form for the line that satisfies each set of conditions.**

1. **Slope = 3, passes through (2, -4)**
   
   **Solution:**
   The point-slope form of a line is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting the values:
   \[
   y - (-4) = 3(x - 2)
   \]
   Simplifying:
   \[
   y + 4 = 3(x - 2)
   \]

2. **Slope = -5, passes through (-9, 7)**

   **Solution:**
   Using the point-slope form:
   \[
   y - 7 = -5(x - (-9))
   \]
   Simplifying:
   \[
   y - 7 = -5(x + 9)
   \]

### Problem 2:
**Write an equation in point-slope form for a line that passes through each set of points.**

3. **(5, 1) and (3, 4)**

   **Solution:**
   First, calculate the slope \( m \) between the two points:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{3 - 5} = \frac{3}{-2} = -\frac{3}{2}
   \]
   Using the point-slope form with point (5, 1):
   \[
   y - 1 = -\frac{3}{2}(x - 5)
   \]

4. **(-3, -7) and (-6, -4)**

   **Solution:**
   Calculate the slope \( m \):
   \[
   m = \frac{-4 - (-7)}{-6 - (-3)} = \frac{-4 + 7}{-6 + 3} = \frac{3}{-3} = -1
   \]
   Using the point-slope form with point (-3, -7):
   \[
   y - (-7) = -1(x - (-3))
   \]
   Simplifying:
   \[
   y + 7 = -(x + 3)
   \]

### Problem 3:
**Application Problems**

5. **(23) Jennifer logs in twice as much as she plans to run for every swimming lap.**
   
   **Note:** The complete problem statement is not fully visible, but the idea seems to involve solving a proportional relationship or system of equations related to swimming and running.

If you want further details or have any questions, feel free to ask!

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### Questions to consider:
1. How can the point-slope form be converted to slope-intercept form?
2. What are the advantages of using point-slope form over slope-intercept form?
3. How would the equations change if you were given the intercepts instead of points?
4. How do you determine the slope of a line given two points?
5. Can a line have an undefined slope, and if so, what would its equation look like?

**Tip:** Remember that when working with the point-slope form, the chosen point on the line does not affect the final equation, as long as the slope is correct!

Explore how to solve equations of lines using the point-slope form with detailed examples. Learn how to write equations of lines given slopes and points, suitable for high school students.

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