Question What is the equation of the line that passes through the point \( (8,6) \) a has a slope of \( \frac{1}{4} \) ? Answer Attempt 1 out of 3

To find the equation of the line, we can use the point-slope form: \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes. Plugging in the given values: \( y - 6 = \frac{1}{4}(x - 8) \). Simplifying this will give you the equation in slope-intercept form as \( y = \frac{1}{4}x + 4 \). Now, why is this important? Understanding how to derive equations from a point and slope is fundamental in many fields, such as physics for motion analysis, economics for trend prediction, and computer graphics for rendering lines. It empowers you to model real-world situations using a simple linear equation!