Write an equation in standard form for the line that passes through the given points. \( (0,4) \) and \( (5,0) \) The equation of the line in standard form is (Type your answer in standard form.)

To find the equation of the line in standard form using the given points \((0,4)\) and \((5,0)\), we first identify the slope \(m\). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{5 - 0} = \frac{-4}{5} \] Using the slope-intercept form \(y = mx + b\) where \(b\) is the y-intercept (which is 4 from point \((0,4)\)), we can write the equation as: \[ y = -\frac{4}{5}x + 4 \] Now to convert this to standard form \(Ax + By = C\): 1. Multiply the entire equation by 5 to eliminate the fraction: \[ 5y = -4x + 20 \] 2. Rearranging gives: \[ 4x + 5y = 20 \] So the equation of the line in standard form is: \[ 4x + 5y = 20 \]