https://file.aiquickdraw.com/mathbot/file/172892415943445flomvj.jpg

https://file.aiquickdraw.com/mathbot/file/172892415943693nap4z9.jpg

Let's work through the problems step-by-step.

### Problems 11-16: Determine if the equations are parallel, perpendicular, or neither.

1. **Problem 11:**
   - Equations: \( y = -3x + 6 \) and \( y = \frac{1}{3}x - 8 \)
   - Slopes: -3 and 1/3
   - **Answer:** Perpendicular (because the slopes are negative reciprocals).

2. **Problem 12:**
   - Equations: \( y = \frac{5}{4}x + 1 \) and \( y = \frac{5}{4}x - 7 \)
   - Slopes: Both are 5/4
   - **Answer:** Parallel (because the slopes are identical).

3. **Problem 13:**
   - Equations: \( 3x + 2y = 6 \) and \( y = -\frac{3}{2}x + 5 \)
   - Rewrite \( 3x + 2y = 6 \) in slope-intercept form:
     \[
     2y = -3x + 6 \quad \Rightarrow \quad y = -\frac{3}{2}x + 3
     \]
   - Slopes: Both are -3/2
   - **Answer:** Parallel (same slopes).

4. **Problem 14:**
   - Equations: \( 3y = 4x + 15 \) and \( 9x + 12y = 12 \)
   - Rewrite both in slope-intercept form:
     \( y = \frac{4}{3}x + 5 \) and \( y = -\frac{3}{4}x + 1 \)
   - Slopes: 4/3 and -3/4
   - **Answer:** Perpendicular (slopes are negative reciprocals).

5. **Problem 15:**
   - Equations: \( 10x - 2y = 16 \) and \( x + 5y = -20 \)
   - Rewrite both in slope-intercept form:
     \( y = 5x - 8 \) and \( y = -\frac{1}{5}x - 4 \)
   - Slopes: 5 and -1/5
   - **Answer:** Perpendicular.

6. **Problem 16:**
   - Equations: \( 5x + 3y = 3 \) and \( 3x + 5y = -25 \)
   - Rewrite both in slope-intercept form:
     \( y = -\frac{5}{3}x + 1 \) and \( y = -\frac{3}{5}x - 5 \)
   - Slopes: -5/3 and -3/5
   - **Answer:** Neither (not equal or negative reciprocals).

---

Would you like to go over the remaining graph and slope-intercept problems?

Determine if the equations are parallel, perpendicular, or neither; and write the equations of the graph in slope-intercept form.

This exercise helps students determine whether pairs of linear equations are parallel, perpendicular, or neither by comparing slopes. It also teaches how to convert equations from standard to slope-intercept form. Includes detailed steps for understanding algebraic concepts of lines and slopes. 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