Write a slope-intercept equation for a line with the given characteristics. \( m=-5 \), passes through \( (-7,8) \) A. \( y=5 x-25 \) B. \( y=-5 x+34 \) C. \( 5 x+y=27 \) D. \( y=-5 x-27 \)

To write the slope-intercept equation \( y = mx + b \) given the slope \( m = -5 \) and a point on the line \( (-7, 8) \), we start by plugging in the values for \( m \), and the coordinates of the point to solve for \( b \): 1. Use the point \( (-7, 8) \): \[ 8 = -5(-7) + b \] \[ 8 = 35 + b \] \[ b = 8 - 35 = -27 \] Putting it all together, we have: \[ y = -5x - 27 \] So the equation of the line is \( D. y = -5x - 27 \). Now for some additional context! The coordinate system we use dates back to the ancient Greeks, but the modern formulation was developed by René Descartes in the 17th century. His Cartesian plane concept allows us to visualize relationships in a very organized way, paving the way for modern algebra and geometry. Moreover, the slope-intercept form is particularly handy in everyday life! For instance, if you're plotting your daily expenses versus income, you can slope your budgetary decisions steeply upward or mildly downward by adjusting the slope (your spending habits) to stay in your financial lane. Always keep an eye on that balance!