Final answer:
The equation of the line through the point (15,5) with slope 15/8 in point-slope form is y - 5 = (15/8)(x - 15). Simplifying, the equation becomes y = (15/8)x - 185/8.
Step-by-step explanation:
To write the equation of a line using point-slope form, we need to know the coordinates of a point on the line and the slope of the line. In this case, the point is (15,5) and the slope is 15/8. The equation can be written as y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point and m is the slope.
Substituting the values into the equation, we get y - 5 = (15/8)(x - 15). Simplifying further, y - 5 = (15/8)x - (225/8). To isolate y, we can add 5 to both sides of the equation, resulting in y = (15/8)x - (225/8) + 5. Combining the constants, y = (15/8)x - 185/8.