The equation of a line is y=4/3(x)-5/3.

**What would be the slope of a line perpendicular to this line?**

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. 

Given the equation of the line:

\[ y = \frac{4}{3}x - \frac{5}{3} \]

we can see that the slope \( m \) of this line is \( \frac{4}{3} \).

To find the slope of a line perpendicular to this one, we take the negative reciprocal of \( \frac{4}{3} \):

\[ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{\frac{4}{3}} = -\frac{3}{4} \]

Therefore, the slope of a line perpendicular to the given line is \( -\frac{3}{4} \).

Do you want more details or have any questions?

Here are 5 questions you can ask next:
1. How do you find the slope of a line given two points?
2. What is the equation of a line parallel to the given line and passing through a specific point?
3. How do you derive the point-slope form of a line's equation?
4. Can you explain how to convert between different forms of a line's equation?
5. How do you determine if two lines are parallel, perpendicular, or neither?

Tip: Remember, perpendicular slopes are always negative reciprocals of each other.

Learn how to find the slope of a line perpendicular to y = 4/3(x) - 5/3 with a step-by-step explanation. This problem covers key concepts in linear equations and perpendicular slopes. Suitable for students in Grades 7-9.

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