What is the slope of the line represented by the equation `6y - 14x = 5`?

Options

A. `-14`
B. `5/6`
C. `7/3`
D. `6`

Answer

To find the slope of the line represented by the equation \(6y - 14x = 5\), we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by the equation:
\[ y = mx + c \]
where \(m\) is the slope and \(c\) is the y-intercept. We need to rearrange the given equation into this form.

### Step 2: Isolate \(y\)
Starting with the original equation:
\[ 6y - 14x = 5 \]
we can add \(14x\) to both sides:
\[ 6y = 14x + 5 \]

### Step 3: Divide by the coefficient of \(y\)
Now, we will divide the entire equation by \(6\) to solve for \(y\):
\[ y = \frac{14}{6}x + \frac{5}{6} \]

### Step 4: Simplify the slope
Next, we simplify \(\frac{14}{6}\):
\[ y = \frac{7}{3}x + \frac{5}{6} \]

### Step 5: Identify the slope
From the equation \(y = \frac{7}{3}x + \frac{5}{6}\), we can see that the slope \(m\) is:
\[ m = \frac{7}{3} \]

Thus, the slope of the line represented by the equation \(6y - 14x = 5\) is \(\frac{7}{3}\).

### Final Answer
The slope of the line is \(\frac{7}{3}\).

---