Find the slope and y-intercept of the line `2x - 3y - 4 = 0`

Answer

To find the slope and y-intercept of the line given by the equation \(2x - 3y - 4 = 0\), 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 start with the given equation:
\[ 2x - 3y - 4 = 0 \]

### Step 2: Isolate \(y\)
To isolate \(y\), we can rearrange the equation:
\[ -3y = -2x + 4 \]
Now, divide every term by \(-3\):
\[ y = \frac{2}{3}x - \frac{4}{3} \]

### Step 3: Identify the slope and y-intercept
Now that we have the equation in the form \(y = mx + c\), we can identify the slope and y-intercept:
- The slope \(m\) is \(\frac{2}{3}\).
- The y-intercept \(c\) is \(-\frac{4}{3}\).

### Final Answer
Thus, the slope of the line is \(\frac{2}{3}\) and the y-intercept is \(-\frac{4}{3}\).

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