The equation of line t is y=
7
4
x+2. Perpendicular to line t is line u, which passes through the point (2,
–
2). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.



To find the equation of line \( u \), which is perpendicular to line \( t \) given by the equation \( y = \frac{7}{4}x + 2 \), we first need to determine the slope of line \( u \).

1. **Determine the slope of line \( t \)**:
   The slope of line \( t \) is \( \frac{7}{4} \).

2. **Find the slope of line \( u \)**:
   The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Thus, the slope of line \( u \) is:
   \[
   m_u = -\frac{1}{\frac{7}{4}} = -\frac{4}{7}
   \]

3. **Use the point-slope form**:
   We know line \( u \) passes through the point \( (2, -2) \). We can use the point-slope form of the equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) = (2, -2) \) and \( m = -\frac{4}{7} \).

   Plugging in the values:
   \[
   y - (-2) = -\frac{4}{7}(x - 2)
   \]
   Simplifying this:
   \[
   y + 2 = -\frac{4}{7}x + \frac{8}{7}
   \]
   \[
   y = -\frac{4}{7}x + \frac{8}{7} - 2
   \]
   Converting \(-2\) to a fraction with a denominator of \(7\):
   \[
   -2 = -\frac{14}{7}
   \]
   Therefore:
   \[
   y = -\frac{4}{7}x + \frac{8}{7} - \frac{14}{7}
   \]
   \[
   y = -\frac{4}{7}x - \frac{6}{7}
   \]

4. **Final equation of line \( u \)**:
   The equation of line \( u \) in slope-intercept form is:
   \[
   y = -\frac{4}{7}x - \frac{6}{7}
   \]

If you have any questions or need further details, let me know! Here are some related questions you might consider:

1. What are the coordinates of another point on line \( u \)?
2. How do you determine if two lines are perpendicular using their slopes?
3. Can you convert the equation of line \( u \) into standard form?
4. How would the equation change if line \( u \) passed through a different point?
5. What is the geometric interpretation of the negative slope of line \( u \)? 

**Tip**: When finding the slope of perpendicular lines, remember to flip the fraction and change the sign!

The equation of line t is y=7/4x+2. Perpendicular to line t is line u, which passes through the point (2,–2). What is the equation of line u?

Discover how to find the equation of line u, perpendicular to line t (y = 7/4x + 2) and passing through the point (2, -2). This solution involves determining slopes, using point-slope form, and simplifying the final equation. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation