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The given task asks to write an equation of a line parallel to \( y = \frac{7}{8}x + 1 \) that passes through the point \( C(3,5) \). 

To solve this:

1. Since the line is parallel to \( y = \frac{7}{8}x + 1 \), it will have the same slope. The slope of this line is \( \frac{7}{8} \).
   
2. The general equation for a line in slope-intercept form is:
   \[
   y = mx + b
   \]
   where \( m \) is the slope and \( b \) is the y-intercept.

3. To find the equation of the new line passing through \( C(3,5) \), we use the point-slope form of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) = (3, 5) \) and \( m = \frac{7}{8} \). Substituting the values:
   \[
   y - 5 = \frac{7}{8}(x - 3)
   \]

4. Simplify the equation:
   \[
   y - 5 = \frac{7}{8}x - \frac{21}{8}
   \]
   \[
   y = \frac{7}{8}x - \frac{21}{8} + 5
   \]
   \[
   y = \frac{7}{8}x - \frac{21}{8} + \frac{40}{8}
   \]
   \[
   y = \frac{7}{8}x + \frac{19}{8}
   \]

Thus, the equation of the line parallel to \( y = \frac{7}{8}x + 1 \) that passes through \( C(3,5) \) is:
\[
y = \frac{7}{8}x + \frac{19}{8}
\]

Would you like any more details or have questions about this?

Here are 5 related questions you might explore:
1. How do you find the slope of a line given two points?
2. What are the different forms of linear equations?
3. How do you convert a line equation from point-slope to slope-intercept form?
4. What is the significance of the y-intercept in the slope-intercept form?
5. How would the equation change if the line were perpendicular instead of parallel?

**Tip:** The slope of parallel lines is always the same, while perpendicular lines have slopes that are negative reciprocals.

Write an equation for the line parallel to the given line that contains C (3,5); y = (7/8)x + 1

Learn how to find the equation of a line parallel to y = (7/8)x + 1 that passes through the point (3,5). This problem covers key algebra concepts, including slope-intercept form and the point-slope form. Ideal for Grades 8-10 students.

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