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The problem asks to find the equation of a line that passes through the point \((3, 7)\) and is parallel to a line passing through the points \((4, 5)\) and \((-5, -2)\).

### Step 1: Find the slope of the given line
To find the slope of the line passing through \((4, 5)\) and \((-5, -2)\), use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points \((4, 5)\) and \((-5, -2)\):

\[
m = \frac{-2 - 5}{-5 - 4} = \frac{-7}{-9} = \frac{7}{9}
\]

The slope of the line passing through \((4, 5)\) and \((-5, -2)\) is \(m = \frac{7}{9}\).

### Step 2: Equation of the parallel line
Since the two lines are parallel, they will have the same slope. Therefore, the line passing through \((3, 7)\) will also have a slope of \(m = \frac{7}{9}\).

The equation of a line can be written in point-slope form:

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

Substitute \(m = \frac{7}{9}\), and the point \((3, 7)\):

\[
y - 7 = \frac{7}{9}(x - 3)
\]

### Step 3: Simplify the equation
Expand and simplify the equation:

\[
y - 7 = \frac{7}{9}x - \frac{21}{9}
\]

\[
y - 7 = \frac{7}{9}x - \frac{7}{3}
\]

Add 7 to both sides:

\[
y = \frac{7}{9}x - \frac{7}{3} + 7
\]

Convert 7 to a fraction with denominator 3:

\[
y = \frac{7}{9}x - \frac{7}{3} + \frac{21}{3}
\]

\[
y = \frac{7}{9}x + \frac{14}{3}
\]

### Final Equation:
The equation of the line passing through \((3, 7)\) and parallel to the line passing through \((4, 5)\) and \((-5, -2)\) is:

\[
y = \frac{7}{9}x + \frac{14}{3}
\]

Would you like further details or have any questions?

Here are some related questions for further practice:
1. How do you find the slope of a line given two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you find the equation of a perpendicular line?
4. Can two lines with different slopes be parallel?
5. How can you convert a point-slope equation to slope-intercept form?

**Tip:** To quickly check if two lines are parallel, just compare their slopes! If the slopes are equal, the lines are parallel.

Find an equation of line passing through the point (3, 7) parallel to the line passing through (4, 5) and (-5, -2).

Learn how to find the equation of a line passing through the point (3, 7) that is parallel to the line passing through (4, 5) and (-5, -2). This problem covers key concepts in coordinate geometry, including calculating slopes and using the point-slope formula. Suitable for students in Grades 8-10.

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