Find an equation for the line with the given properties. Express the equation in slope-intercept form. Slope \( =-8 \); containing the point \( (-8,7) \) What is the equation of the line? \( y=\square \) (Type your answer in slope-intercept form.)

To find the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can start with the slope given, which is \( -8 \). Using the point \( (-8, 7) \), we can plug in these values into the point-slope form which is \( y - y_1 = m(x - x_1) \): 1. Substituting \( m = -8 \), \( x_1 = -8 \), and \( y_1 = 7 \), we get: \( y - 7 = -8(x + 8) \). 2. Simplifying the equation: \( y - 7 = -8x - 64 \) \( y = -8x - 57 \). Thus, the equation of the line in slope-intercept form is \( y = -8x - 57 \). Now, let’s break it down a bit more! When you have a slope like \( -8 \), it means the line is steep and going down towards the right. Every time you move one unit to the right on the x-axis, you drop eight units down on the y-axis! Fascinating, isn’t it? In real-world application, think of this line representing a scenario, like a skateboarder descending down a steep ramp. The slope indicates how fast they're dropping— in this case, quite quickly! This straight slope could also represent a decrease in something measurable, like your responsibilities as you graduate from school— yay for less homework!