Which equation is perpendicular to the graph of 4x -3y = 10

To find the equation of a line that is **perpendicular** to the graph of the given line \(4x - 3y = 10\), follow these steps:

1. **Convert the given equation to slope-intercept form** \(y = mx + b\), where \(m\) is the slope.
   
   Start by isolating \(y\):
   \[
   4x - 3y = 10
   \]
   Subtract \(4x\) from both sides:
   \[
   -3y = -4x + 10
   \]
   Now, divide by \(-3\):
   \[
   y = \frac{4}{3}x - \frac{10}{3}
   \]
   So, the slope of the given line is \(m = \frac{4}{3}\).

2. **Find the slope of the perpendicular line**. 

   The slope of a line perpendicular to another is the **negative reciprocal** of the original slope. The negative reciprocal of \(\frac{4}{3}\) is \(-\frac{3}{4}\).

3. **Form the equation of the perpendicular line** using the slope \(m = -\frac{3}{4}\). 

   The general form of a line is:
   \[
   y = mx + b
   \]
   Substituting the perpendicular slope:
   \[
   y = -\frac{3}{4}x + b
   \]
   You can plug in any point or solve for \(b\) if a specific point is provided, but without additional information, the general form is:
   \[
   y = -\frac{3}{4}x + b
   \]
   
Thus, the equation of any line perpendicular to the given one will have the slope \(-\frac{3}{4}\).

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Would you like more details on this, or do you have any specific questions?

Here are 5 related questions:
1. How can I find the equation of a perpendicular line passing through a specific point?
2. What does the negative reciprocal mean in terms of slopes?
3. How can I convert between different forms of linear equations?
4. What is the relationship between parallel and perpendicular slopes?
5. How do I find the intersection point of two perpendicular lines?

**Tip:** When dealing with perpendicular lines, always remember that their slopes are negative reciprocals of each other.

Which equation is perpendicular to the graph of 4x - 3y = 10?

Discover how to find the equation of a line perpendicular to 4x - 3y = 10. This solution covers key algebraic concepts, including the slope-intercept form and the negative reciprocal rule for perpendicular slopes. Suitable for students in Grades 9-11.

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