For equations given below find the slope and the y- intercept.
` x- 3y - 8=0`

Answer

To find the slope and the y-intercept of the equation \( x - 3y - 8 = 0 \), we can follow these steps:

### Step 1: Rearrange the equation into 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.

Starting with:
\[ x - 3y - 8 = 0 \]

We can isolate \( y \) by moving \( x \) and \( -8 \) to the other side:
\[ -3y = -x + 8 \]

### Step 2: Solve for \( y \)
Now, divide every term by \(-3\) to solve for \( y \):
\[ y = \frac{1}{3}x - \frac{8}{3} \]

### Step 3: Identify the slope and y-intercept
Now that we have the equation in the form \( y = mx + c \):
- The slope \( m \) is \( \frac{1}{3} \).
- The y-intercept \( c \) is \( -\frac{8}{3} \).

### Final Answer
- Slope: \( \frac{1}{3} \)
- Y-intercept: \( -\frac{8}{3} \)

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