Final answer:
The y-intercept (b) of the line passing through (-2, 8) and perpendicular to y = 2x + 52 is 7. Answer: 7 (c).
Step-by-step explanation:
To find the y-intercept (b) of a line perpendicular to y = 2x + 52, we need to determine the equation of the new line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The given line has a slope of 2, and the line perpendicular to it will have a negative reciprocal slope.
The negative reciprocal of 2 is -1/2, so the slope of the new line is -1/2.
Now we can use the coordinates of the point (-2, 8) to find the y-intercept. Substitute the values into the slope-intercept form and solve for b:
8 = (-1/2)(-2) + b
8 = 1 + b
b = 8 - 1
b = 7
Therefore, the y-intercept (b) of the line passing through (-2, 8) and perpendicular to y = 2x + 52 is 7.