A line with a slope of \( -\frac{1}{8} \) passes through the point \( (7,6) \). What is its equation in point-slope form? Use the specifled point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions. \( y y=\square=\square \)

To write the equation in point-slope form, we start with the formula \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is the given point and \( m \) is the slope. Here, \( m = -\frac{1}{8} \), \( x_1 = 7 \), and \( y_1 = 6 \). Plugging in the values, we get: \[ y - 6 = -\frac{1}{8}(x - 7) \] Now, for a little historical background, point-slope form is a handy tool that dates back to the early study of algebra and calculus. It allows for an easy way to express linear relationships, making it a fundamental skill in mathematics since the days of ancient Greek mathematicians! And speaking of fun applications, think of graphing this equation! With a slope of \(-\frac{1}{8}\), this line is a gentle downhill slope—like a slight decline in a snow sledding hill. Perfect for those cozy winter afternoons or even analyzing trends in data where consistent, gradual changes occur!