Final Answer:
To make the lines perpendicular, the correct slope for the second line is -2: y = -2x + 7
Step-by-step explanation:
Identify Slope of the First Line:
The given line is y = (1/2)x + 5. The slope (m) of this line is 1/2.
Reciprocal to Find Perpendicular Slope:
For two lines to be perpendicular, the product of their slopes must be -1.
The reciprocal of 1/2 is 2. So, the desired slope for the second line is -2.
Write Equation for Second Line:
The second line is y = mx + 7, and the desired slope is -2. So, the equation is y = -2x + 7.
Therefore, to make the lines perpendicular, the slope for the second line should be -2, and its equation is y = -2x + 7.