Determine the slope of a line perpendicular to `-3x+5y=20`

Options

A. `-4`
B. `-5/3`
C. `3/5`
D. `1/4`

Answer

To determine the slope of a line that is perpendicular to the line given by the equation \(-3x + 5y = 20\), we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation:
\[ -3x + 5y = 20 \]
We want to isolate \(y\) to express the equation in the form \(y = mx + c\), where \(m\) is the slope.

### Step 2: Move \(-3x\) to the other side
Add \(3x\) to both sides:
\[ 5y = 3x + 20 \]

### Step 3: Divide by 5 to solve for \(y\)
Now, divide every term by 5:
\[ y = \frac{3}{5}x + 4 \]
From this equation, we can see that the slope \(m\) of the original line is \(\frac{3}{5}\).

### Step 4: Find the slope of the perpendicular line
The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, we need to take the negative reciprocal of \(\frac{3}{5}\).

To find the negative reciprocal:
\[ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{\frac{3}{5}} = -\frac{5}{3} \]

### Final Answer
Thus, the slope of the line that is perpendicular to the line given by the equation \(-3x + 5y = 20\) is:
\[ \boxed{-\frac{5}{3}} \]