Find the slope and the \( y \)-intercept of the line. \[ 4 x-3 y=-15 \] Write your answers in simplest form.
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To find the slope and the \( y \)-intercept, we need to rearrange the equation into the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Starting with the given equation: \[ 4x - 3y = -15 \] First, isolate \( y \): \[ -3y = -4x - 15 \] Now, divide by -3: \[ y = \frac{4}{3}x + 5 \] From this, we can see that the slope \( m \) is \( \frac{4}{3} \) and the \( y \)-intercept \( b \) is \( 5 \). Therefore, the slope is \( \frac{4}{3} \) and the \( y \)-intercept is \( (0, 5) \).