Find the slope and the y- intercept of the line:
` (x)/(3) -(y)/(5) =1`

Answer

To find the slope and the y-intercept of the line given by the equation \(\frac{x}{3} - \frac{y}{5} = 1\), 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 given equation:
\[ \frac{x}{3} - \frac{y}{5} = 1 \]

### Step 2: Isolate \(y\)
First, we can move \(\frac{y}{5}\) to the right side:
\[ -\frac{y}{5} = 1 - \frac{x}{3} \]

Next, multiply through by -1 to make \(y\) positive:
\[ \frac{y}{5} = -1 + \frac{x}{3} \]

### Step 3: Multiply by 5 to solve for \(y\)
Now, multiply the entire equation by 5 to eliminate the fraction:
\[ y = 5\left(-1 + \frac{x}{3}\right) \]
\[ y = -5 + \frac{5x}{3} \]

### Step 4: Identify the slope and y-intercept
Now, we can compare this with the slope-intercept form \(y = mx + c\):
\[ y = \frac{5}{3}x - 5 \]

From this, we can see that:
- The slope \(m = \frac{5}{3}\)
- The y-intercept \(c = -5\)

### Final Answer
- Slope: \(\frac{5}{3}\)
- Y-intercept: \(-5\)

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