Explanation:
To find the equation of a line that is parallel to the line 2y = 3x + 10, we need to determine the slope of the given line.
The equation 2y = 3x + 10 can be rewritten in slope-intercept form as y = (3/2)x + 5.
From this equation, we can see that the slope of the given line is 3/2.
Since we want to find a line that is parallel to this line, the parallel line will also have a slope of 3/2.
Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the parallel line.
We are given that the line passes through the point (2,-5). Plugging in the values x = 2 and y = -5 into the equation, we can solve for b.
-5 = (3/2)(2) + b
-5 = 3 + b
b = -8
Therefore, the equation of the line that passes through (2,-5) and is parallel to the line 2y = 3x + 10 is y = (3/2)x - 8.