Find the slope and the y- intercept of the line:
` (2x) /( 5)+(3y)/(4) = 1`

Answer

To find the slope and the y-intercept of the line given by the equation \( \frac{2x}{5} + \frac{3y}{4} = 1 \), we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. We need to isolate \( y \) in the given equation.

Starting with:
\[ \frac{2x}{5} + \frac{3y}{4} = 1 \]

### Step 2: Isolate the term with \( y \)
Subtract \( \frac{2x}{5} \) from both sides:
\[ \frac{3y}{4} = 1 - \frac{2x}{5} \]

### Step 3: Eliminate the fraction by multiplying by 4
Multiply every term by 4 to eliminate the fraction:
\[ 3y = 4 \left(1 - \frac{2x}{5}\right) \]
This simplifies to:
\[ 3y = 4 - \frac{8x}{5} \]

### Step 4: Divide by 3 to solve for \( y \)
Now, divide every term by 3:
\[ y = \frac{4}{3} - \frac{8}{15}x \]

### Step 5: Identify the slope and y-intercept
Now the equation is in the form \( y = mx + c \):
- The slope \( m \) is \( -\frac{8}{15} \)
- The y-intercept \( c \) is \( \frac{4}{3} \)

### Final Answer
- Slope: \( -\frac{8}{15} \)
- Y-intercept: \( \frac{4}{3} \)

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