For each of the equations given below, find the 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.

### Step 2: Isolate \( y \)
Starting with the original equation:
\[ x + 3y + 5 = 0 \]
we first move \( x \) and \( 5 \) to the right side:
\[ 3y = -x - 5 \]

### Step 3: Divide by the coefficient of \( y \)
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 that we have the equation in the form \( y = mx + c \):
- The slope \( m \) is \( -\frac{1}{3} \).
- The y-intercept \( c \) is \( -\frac{5}{3} \).

### Final Answer
- Slope \( m = -\frac{1}{3} \)
- Y-intercept \( c = -\frac{5}{3} \)

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