which equation represents a line which is perpendicular to the line y=-6/5x-7

To find the equation of a line perpendicular to the line \( y = -\frac{6}{5}x - 7 \), we need to focus on the slopes. 

The slope of the given line is \( -\frac{6}{5} \).

For two lines to be perpendicular, the product of their slopes must equal \(-1\). So, if the slope of the given line is \( m_1 = -\frac{6}{5} \), the slope of the perpendicular line \( m_2 \) must satisfy:

\[
m_1 \times m_2 = -1
\]

Substitute the value of \( m_1 \):

\[
-\frac{6}{5} \times m_2 = -1
\]

Solve for \( m_2 \):

\[
m_2 = \frac{5}{6}
\]

Thus, the slope of the line perpendicular to the given line is \( \frac{5}{6} \).

### General Equation of the Perpendicular Line:
The equation of a line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept. Using the slope \( m = \frac{5}{6} \), the equation of a line perpendicular to the given line will have the form:

\[
y = \frac{5}{6}x + b
\]

To fully determine the equation, you would need the y-intercept or a point that the line passes through. If no specific point is given, this is the general form of a perpendicular line.

Would you like further details on finding the y-intercept or more information on perpendicular lines?

### Related Questions:
1. How do you find the slope of a line from its equation?
2. What is the relationship between parallel and perpendicular slopes?
3. How can you determine if two lines are perpendicular using their equations?
4. How do you find the equation of a line passing through two points?
5. How do you solve a system of equations involving perpendicular lines?

**Tip**: Perpendicular lines always have slopes that are negative reciprocals of each other.

Which equation represents a line which is perpendicular to the line y=-6/5x-7?

Discover how to determine the equation of a line that is perpendicular to y = -6/5x - 7. This guide covers key algebraic concepts such as slopes, perpendicular lines, and the relationship between negative reciprocals. Perfect for students in Grades 8-10.

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