Which equation represents a line which is parallel to the line Y equals 8X -7        A: 8X -7=1 B: 8Y-x=24

To determine which equation represents a line parallel to the line \( Y = 8X - 7 \), we need to understand that parallel lines have the same slope.

The slope of the given line is 8 (since the equation is in slope-intercept form \( Y = mX + b \), where \( m \) is the slope).

Now, let's analyze the two options:

- **Option A: \( 8X - 7 = 1 \)**  
   This is not an equation in the form of a line, and it does not clearly represent a linear relationship with a slope. It seems more like an equation with constants rather than a line equation.

- **Option B: \( 8Y - X = 24 \)**  
   We need to rewrite this in slope-intercept form (i.e., \( Y = mX + b \)):
   \[
   8Y = X + 24 \implies Y = \frac{1}{8}X + 3
   \]
   Here, the slope is \( \frac{1}{8} \), which is different from the slope of 8 in the original line.

### Conclusion:
Neither option A nor option B represents a line parallel to \( Y = 8X - 7 \), as neither has the slope of 8. 

If you would like more details on how to identify parallel lines or how to rewrite equations in slope-intercept form, feel free to ask!

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**Relative Questions:**

1. How can you find the slope of a line from its equation?
2. What is the general condition for two lines to be parallel?
3. How do you rewrite an equation in slope-intercept form?
4. Can you explain how different slopes affect the orientation of lines on a graph?
5. What is the meaning of the \( y \)-intercept in a linear equation?

**Tip:** For two lines to be parallel, their slopes must be equal. Always compare the slope values when checking for parallelism.

Which equation represents a line which is parallel to the line Y equals 8X - 7? A: 8X -7=1 B: 8Y-X=24

Explore how to identify an equation that represents a line parallel to Y = 8X - 7. This problem involves key algebraic concepts like slope-intercept form and the condition for parallel lines, making it ideal for students in Grades 8-10.

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