What is the slope of a line perpendicular to the line ?
a.)
b.) -4
c.)
d.)

Ask by Simmons Lowe. in the United States

Jan 26,2025

Question

What is the slope of a line perpendicular to the line $$ y=\frac{12}{5} x+4 $$ ? a.) $$ -\frac{1}{4} $$ b.) -4 c.) $$ -\frac{12}{5} $$ d.) $$ -\frac{5}{12} $$

UpStudy AI · Accepted Answer

To determine the slope of a line perpendicular to the given line $$ y = \frac{12}{5}x + 4 $$, follow these steps:

1. **Identify the Slope of the Given Line:**
   
   The equation is in the slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope. 
   
   So, the slope ($$ m $$) of the given line is:
   $$
   m = \frac{12}{5}
   $$

2. **Find the Negative Reciprocal:**
   
   For two lines to be perpendicular, the slope of one line must be the **negative reciprocal** of the other.

The negative reciprocal of $$ \frac{12}{5} $$ is:
   $$
   -\frac{5}{12}
   $$

3. **Select the Correct Option:**
   
   Comparing with the provided choices:
   $$
   \text{d.) } -\frac{5}{12}
   $$
   
   This matches our calculation.

**Answer:**  
d.) $$ -\frac{5}{12} $$
The slope of the perpendicular line is $$ -\frac{5}{12} $$.

What is the slope of a line perpendicular to the line ?
a.)
b.) -4
c.)
d.)

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What is the slope of a line perpendicular to the line ? a.) b.) -4 c.) d.)