Are y=-6x+25 and y=6x-23 perpendicular to each other

To determine if two lines are perpendicular, we need to examine their slopes. The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

where \(m\) is the slope.

Let's compare the slopes of the two lines:

1. For the line \(y = -6x + 25\), the slope is \(m_1 = -6\).
2. For the line \(y = 6x - 23\), the slope is \(m_2 = 6\).

Two lines are perpendicular if the product of their slopes equals \(-1\). In other words, \(m_1 \times m_2 = -1\).

Now, calculate the product of the slopes:

\[
m_1 \times m_2 = (-6) \times 6 = -36
\]

Since \(-36\) is not equal to \(-1\), the lines are **not perpendicular**.

Would you like more details, or do you have any other questions? Here are five related questions you might find useful:

1. How do you find the slope of a line from its equation?
2. What does it mean for two lines to be parallel?
3. Can two lines with the same slope ever be perpendicular?
4. How can you verify if two lines intersect at a specific point?
5. What are the conditions for two lines to be coincident?

**Tip:** When checking if lines are perpendicular, always focus on the product of their slopes being \(-1\).

Are y=-6x+25 and y=6x-23 perpendicular to each other?

Explore how to determine if two lines, y=-6x+25 and y=6x-23, are perpendicular by comparing their slopes. This problem covers algebraic concepts related to linear equations and the condition for perpendicularity. Suitable for students in Grades 8-10.

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