Final answer:
The equation for the line is y = (3/2)x - 1.
Step-by-step explanation:
The equation for the line with a rate of change of 3/2 can be written in slope-intercept form as y = (3/2)x + b, where b is the y-intercept. To find the equation of the line, we need to find the value of b.
Since the line passes through the point (8,7), we can substitute these coordinates into the equation and solve for b. So, 7 = (3/2)(8) + b. Simplifying the equation, b = -1.
Therefore, the equation for the line is y = (3/2)x - 1