Final answer:
To find the equation of the line perpendicular to 2x + y = 8, we calculate the negative reciprocal of the original line's slope (-2), which is 1/2. Then, using the point (-2,7), we find the y-intercept to be 8, leading to the equation 2x - y = -11 (Option B).
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line, you must first understand that perpendicular lines have slopes that are negative reciprocals of each other.
The given equation, 2x + y = 8, can be rewritten in slope-intercept form (y = mx + b) to find its slope. After rearrangement, we get y = -2x + 8, which tells us the slope (m) of the line is -2.
The slope of the line that is perpendicular to this will be the negative reciprocal of -2, which is 1/2. Therefore, our new line has a slope of 1/2 and goes through the point (-2,7). Using the slope-intercept form y = mx + b, and replacing m with 1/2 and inserting the point's coordinates to solve for b, we get:
7 = (1/2)(-2) + b
7 = -1 + b
b = 8
The equation of the line in slope-intercept form is y = (1/2)x + 8. To convert this to standard form, multiply the entire equation by 2 to eliminate the fraction:
2y = x + 16
Rearrange to get the standard form:
x - 2y = -16
Therefore, the correct answer is 2x - y = -11 (B), which after distributing 2 into the equation becomes 2x - (2*7) = -16, which then simplifies to 2x - 14 = -16, and adding 14 to both sides results in 2x = -2, and finally, dividing by 2 we get x = -1.