For each of the following given below, find th slope and the y-intercept.
`x+3y+5=0`

Answer

To find the slope and the y-intercept of the equation \( x + 3y + 5 = 0 \), 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 need to rearrange the given equation into this form.

Starting with the equation:
\[ x + 3y + 5 = 0 \]

### Step 2: Isolate \( y \)
To isolate \( y \), we first move \( x \) and \( 5 \) to the other side of the equation:
\[ 3y = -x - 5 \]

### Step 3: Solve for \( y \)
Next, we divide every term by \( 3 \) to solve for \( y \):
\[ y = -\frac{1}{3}x - \frac{5}{3} \]

### Step 4: Identify the slope and y-intercept
Now, we can compare this equation with the slope-intercept form \( y = mx + c \):
- The slope \( m \) is \( -\frac{1}{3} \).
- The y-intercept \( c \) is \( -\frac{5}{3} \).

### Final Answer
Thus, the slope is \( -\frac{1}{3} \) and the y-intercept is \( -\frac{5}{3} \).

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