Final answer:
The equation of the line passing through the points (13,5) and (-3,9) is 4y - x = 28.
Step-by-step explanation:
The equation of the line passing through the points (13,5) and (-3,9) can be found using the slope-intercept form.
First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (9 - 5) / (-3 - 13) = 4 / -16 = -1/4.
Next, substitute the slope (m) and one of the given points into the point-slope form of a linear equation (y - y1) = m(x - x1). Using the point (13,5), we have y - 5 = (-1/4)(x - 13).
Simplifying the equation gives us the standard form: 4y - x = 28