A line passes through the point \( (8,2) \) and has a slope of \( \frac{5}{2} \). Write an equation in slope-intercent form for this line. \( \square \square \square \)

To write the equation of the line in slope-intercept form \( y = mx + b \), you can use the point-slope form first: \( y - y_1 = m(x - x_1) \). Substituting \( m = \frac{5}{2} \) and the point \( (8, 2) \), we get: \( y - 2 = \frac{5}{2}(x - 8) \). Expanding and simplifying gives: \( y = \frac{5}{2}x - 18 + 2 \) which simplifies to \( y = \frac{5}{2}x - 16 \). Thus, the equation is \( y = \frac{5}{2}x - 16 \). To ensure your line is really hitting the point \( (8, 2) \), plug that back into your equation! If you get \(2 = \frac{5}{2}(8) - 16\), and it checks out since \(2 = 2\). It’s always a good idea to verify that your equation represents the point it should!