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!