4. Write the equation of a line that passes through the point

(22, 7) and is perpendicular to a line that passes through the

points (26, 1) and (0, 4).

5. A pair of perpendicular lines intersect at the point (5, 9). Write

the equation of the line that is perpendicular to the line that

also passes through point (24, 4).

A1_M02_T01_L07_Student Lesson.indd 319 5/26/21 2:40 Pm

### Problem 4: Equation of a Line Perpendicular to a Given Line

We are tasked with finding the equation of a line passing through the point \((22, 7)\) and perpendicular to a line passing through the points \((26, 1)\) and \((0, 4)\).

1. **Find the slope of the given line** passing through \((26, 1)\) and \((0, 4)\).
   The slope formula is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the values:
   \[
   m = \frac{4 - 1}{0 - 26} = \frac{3}{-26} = -\frac{3}{26}
   \]
   The slope of the line through \((26, 1)\) and \((0, 4)\) is \(-\frac{3}{26}\).

2. **Find the slope of the perpendicular line**. The slope of a perpendicular line is the negative reciprocal of the original slope. If the slope of the original line is \(-\frac{3}{26}\), the slope of the perpendicular line is:
   \[
   m_{\perp} = \frac{26}{3}
   \]

3. **Write the equation of the perpendicular line** using the point-slope form of a line, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is \((22, 7)\) and \(m_{\perp} = \frac{26}{3}\):
   \[
   y - 7 = \frac{26}{3}(x - 22)
   \]
   Simplify the equation:
   \[
   y - 7 = \frac{26}{3}x - \frac{26}{3} \times 22
   \]
   \[
   y - 7 = \frac{26}{3}x - \frac{572}{3}
   \]
   Add 7 to both sides:
   \[
   y = \frac{26}{3}x - \frac{572}{3} + 7
   \]
   Convert 7 to have a denominator of 3:
   \[
   y = \frac{26}{3}x - \frac{572}{3} + \frac{21}{3}
   \]
   \[
   y = \frac{26}{3}x - \frac{551}{3}
   \]
   Therefore, the equation of the line perpendicular to the given line and passing through the point \((22, 7)\) is:
   \[
   y = \frac{26}{3}x - \frac{551}{3}
   \]

### Problem 5: Equation of a Line Perpendicular to a Given Line

We are tasked with finding the equation of a line that passes through the point \((24, 4)\) and is perpendicular to a line that intersects at the point \((5, 9)\).

1. **Find the slope of the given line**. We do not have a second point, but the problem mentions perpendicular lines. We assume the line's slope is unknown, but we'll denote it as \(m\). If the equation of the first line were available, we'd find the slope of the perpendicular line using the negative reciprocal.

2. Using the **point-slope form**, we have:
   \[
   y - y_1 = m_{\perp}(x - x_1)
   \]
   We need more information about the given line’s slope (or points on the line).

Would you like more details or to clarify the second question?

Here are five related questions:
1. How do you find the slope between two points on a line?
2. What is the negative reciprocal of a number?
3. How do you convert point-slope form to slope-intercept form?
4. What is the relationship between perpendicular lines?
5. How do you handle horizontal and vertical lines when finding perpendicular slopes?

**Tip**: The slope of a line is undefined when it is vertical, and its perpendicular line will be horizontal.

4. Write the equation of a line that passes through the point (22, 7) and is perpendicular to a line that passes through the points (26, 1) and (0, 4). 5. A pair of perpendicular lines intersect at the point (5, 9). Write the equation of the line that is perpendicular to the line that also passes through point (24, 4).

Learn how to write the equation of a line passing through specific points and perpendicular to another line. This problem involves concepts such as finding slopes, calculating negative reciprocals, and using the point-slope form of a line. Suitable for students in 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