A line passes through point \( (6,2) \) and has a slope of \( -\frac{5}{2} \) Write an equation in \( A x+B y=C \) form for this line. Use integers for \( A, B \), and \( C \).

To find the equation of the line in the form \( Ax + By = C \), we can start with the point-slope form of the equation, which is given by: \[ y - y_1 = m(x - x_1) \] Here, \( (x_1, y_1) = (6, 2) \) and the slope \( m = -\frac{5}{2} \). Plugging in these values, we have: \[ y - 2 = -\frac{5}{2}(x - 6) \] Distributing the slope on the right side: \[ y - 2 = -\frac{5}{2}x + 15 \] Adding 2 to both sides gives us: \[ y = -\frac{5}{2}x + 17 \] Now, to convert this into the \( Ax + By = C \) form, we can rearrange it: \[ \frac{5}{2}x + y = 17 \] To eliminate the fraction, we can multiply the entire equation by 2: \[ 5x + 2y = 34 \] Thus, the equation in \( Ax + By = C \) form is: \[ 5x + 2y = 34 \]