Questions: Find the slope and the y-intercept of the line with the following equation. 5x+4y=16 Find the slope of the line. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is -5/4. (Simplify your answer.) B. The slope is undefined. A. The y-intercept is . (Simplify your answer. Type an ordered pair.) B. There is no y-intercept.

Solution Steps

The given equation is: \[ 5x + 4y = 16 \]

To find the slope and the \( y \)-intercept, we need to rewrite this equation in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

First, isolate \( y \) on one side of the equation: \[ 4y = -5x + 16 \]

Next, divide every term by 4: \[ y = -\frac{5}{4}x + 4 \]

From the equation \( y = -\frac{5}{4}x + 4 \), we can identify the slope \( m \) and the \( y \)-intercept \( b \).

The slope \( m \) is: \[ m = -\frac{5}{4} \]

The \( y \)-intercept \( b \) is: \[ b = 4 \]

Final Answer