To determine the slope of a line perpendicular to the line given by the equation [tex]\( y = -\frac{7}{4}x \)[/tex], we must follow these steps:
1. Identify the slope of the given line:
The given line is [tex]\( y = -\frac{7}{4}x \)[/tex]. The slope [tex]\( m \)[/tex] of this line is [tex]\( -\frac{7}{4} \)[/tex].
2. Find the slope of the perpendicular line:
The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. To find the negative reciprocal, switch the numerator and denominator of the original slope and change its sign.
3. Calculate the negative reciprocal:
The slope of the given line is [tex]\( -\frac{7}{4} \)[/tex]. Its negative reciprocal is:
[tex]\[
-\left( \frac{1}{-\frac{7}{4}} \right) = \frac{4}{7}
\][/tex]
Therefore, the slope of the line perpendicular to [tex]\( y = -\frac{7}{4}x \)[/tex] is [tex]\( \frac{4}{7} \)[/tex].
4. Select the correct answer:
Comparing [tex]\( \frac{4}{7} \)[/tex] with the answer choices provided:
- A. [tex]\( -\frac{7}{4} \)[/tex]
- B. [tex]\( \frac{4}{7} \)[/tex]
- C. [tex]\( -\frac{4}{7} \)[/tex]
- D. [tex]\( \frac{7}{4} \)[/tex]
The correct answer is:
B. [tex]\( \frac{4}{7} \)[/tex]
