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To find the slope of the line given by the equation \(7x - 8y = 0\), we need to rewrite it in slope-intercept form, which is:

\[
y = mx + b
\]

where \(m\) represents the slope and \(b\) represents the y-intercept.

Let's manipulate the equation:

1. Start with the original equation:
\[
7x - 8y = 0
\]

2. Solve for \(y\):
\[
-8y = -7x
\]
\[
y = \frac{7}{8}x
\]

Now, the equation is in slope-intercept form. The slope \(m\) is the coefficient of \(x\), which is:

\[
m = \frac{7}{8}
\]

Thus, the slope of the line is \( \frac{7}{8} \).

Would you like further details or have any questions?

Here are five related questions to explore:

1. How would the slope change if the equation were \(7x + 8y = 0\)?
2. What is the y-intercept of the line \(7x - 8y = 0\)?
3. How would you find the slope of a vertical line?
4. How does the slope of this line compare to the slope of the line \(y = 2x + 3\)?
5. What does a slope of zero represent in terms of the orientation of a line?

**Tip:** The slope of a line describes how steep it is. The greater the absolute value of the slope, the steeper the line.

Find the slope of the line determined by the equation 7x - 8y = 0. Simplify your answer.

This lesson explains how to find the slope of a line from the equation 7x - 8y = 0. Learn to rewrite it in slope-intercept form and identify the slope as 7/8. Suitable for students in Grades 8-10.

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