Final answer:
The equation in slope-intercept form that is parallel to y = -5/2x + 3 and passes through the point (5,2) is y = -5/2x + 29/2. Hence, the correct answer is option B.
Step-by-step explanation:
To find the equation of a line that is parallel to y = -5/2x + 3 and passes through the point (5,2), we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. Since the given line is parallel to the desired line, it will have the same slope. Therefore, the equation will have the form y = -5/2x + b. To find b, we substitute the coordinates of the given point into the equation and solve for b. Substituting (5,2) into the equation, we get 2 = -5/2(5) + b. Simplifying, we get 2 = -25/2 + b. Adding 25/2 to both sides of the equation, we get b = 25/2 + 2 = 29/2. Therefore, the equation in slope-intercept form that is parallel to y = -5/2x + 3 and passes through the point (5,2) is y = -5/2x + 29/2. Hence, the correct answer is option B.