The slope of the line parallel to the line whose equation is 2x+3y=8 is

Options

A. `-2`
B. `-(3)/(2)`
C. `-(2)/(3)`
D. `(2)/(3)`

Explanation

To find the slope of the line parallel to the line given by the equation \(2x + 3y = 8\), we can follow these steps:

### Step 1: Write the equation of the line
The equation of the line is given as:
\[ 2x + 3y = 8 \]

### Step 2: Rearrange the equation to slope-intercept form
We need to rearrange this equation into the slope-intercept form, which is \(y = mx + c\), where \(m\) is the slope.

Starting with the original equation:
\[ 2x + 3y = 8 \]

Subtract \(2x\) from both sides:
\[ 3y = -2x + 8 \]

Now, divide every term by \(3\) to isolate \(y\):
\[ y = -\frac{2}{3}x + \frac{8}{3} \]

### Step 3: Identify the slope
In the equation \(y = mx + c\), the coefficient of \(x\) is the slope \(m\). From our rearranged equation, we can see that:
\[ m = -\frac{2}{3} \]

### Step 4: Determine the slope of the parallel line
Since parallel lines have the same slope, the slope of the line \(L_2\) that is parallel to line \(L_1\) will also be:
\[ m_2 = m_1 = -\frac{2}{3} \]

### Final Answer
The slope of the line parallel to the line whose equation is \(2x + 3y = 8\) is:
\[ -\frac{2}{3} \]

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