Write an equation of the line with slope 5 and passing through \( (-1,5) \). Write the equation in standard form. Choose the correct answer below. A. \( x+5 y=10 \) B. \( x-5 y=-10 \) C. \( 5 x+y=10 \) D. \( 5 x-y=-10 \)

To find the equation of the line with a slope of 5 that passes through the point \((-1, 5)\), we can start with the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through. Here, \(m = 5\), \(x_1 = -1\), and \(y_1 = 5\). Substituting these values into the point-slope form gives: \[ y - 5 = 5(x + 1) \] Now, we can simplify this equation: \[ y - 5 = 5x + 5 \] Adding 5 to both sides: \[ y = 5x + 10 \] Next, we need to convert this equation into standard form, which is typically written as \(Ax + By = C\). We can rearrange the equation: \[ -5x + y = 10 \] To write it in standard form with \(A\) as a positive integer, we can multiply the entire equation by -1: \[ 5x - y = -10 \] Now, we can compare this with the options provided: A. \( x + 5y = 10 \) B. \( x - 5y = -10 \) C. \( 5x + y = 10 \) D. \( 5x - y = -10 \) The correct answer is: **D. \( 5x - y = -10 \)**.