Which equation represents a line which is perpendicular to the line y = -1/8x + 3?
A. 8x + y = 6
B. x - 8y = 40
C. x + 8y = 40
D. y - 8x = -2
To find a line that is perpendicular to the line y = -1/8x + 3, we need to determine the slope of the given line. The given line is in the form y = mx + b, with m representing the slope. In this case, the slope of the given line is -1/8.
To find the slope of a line perpendicular to this, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of -1/8 is 8/1, or simply 8.
Now that we know the slope of the line we are looking for, we can examine the answer choices.
A. 8x + y = 6 does not have a slope of 8, so it is not perpendicular to the given line.
B. x - 8y = 40 can be rearranged to the slope-intercept form y = mx + b by isolating y: y = (1/8)x - 5. The slope of this line is 1/8, not 8, so it is not perpendicular to the given line.
C. x + 8y = 40 can be rearranged to y = (-1/8)x + 5, which has a slope of -1/8, not 8. Therefore, it is not perpendicular to the original line.
D. y - 8x = -2 can be rearranged to the slope-intercept form y = mx + b by isolating y: y = 8x - 2. The slope of this line is 8, which matches the negative reciprocal of the slope of the given line, so it is perpendicular to the original line.
Therefore, the correct answer is D. y - 8x = -2.
To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line.
The given line has a slope of -1/8.
To find the negative reciprocal, we flip the fraction and change the sign.
Therefore, the negative reciprocal of -1/8 is 8/1, which simplifies to 8.
Now, we can choose the option that has a slope of 8.
Looking at the answer choices:
A. 8x + y = 6 (simplified slope: -1/8)
B. x - 8y = 40 (simplified slope: 1/8)
C. x + 8y = 40 (simplified slope: -1/8)
D. y - 8x = -2 (simplified slope: -8/1)
The only option with a slope of 8 is D. Therefore, the correct answer is D.
To find a line that is perpendicular to another line, we need to determine the slope of the given line.
The given equation is in the form of y = mx + b, where m represents the slope of the line. In this case, the given line has a slope of -1/8.
To find a line that is perpendicular to this line, we need to use the negative reciprocal of the given slope. The negative reciprocal of -1/8 is 8/1 or simply 8.
Now, let's analyze the answer choices:
A. 8x + y = 6: This equation is not in the form y = mx + b. To check if the slope is perpendicular, rearrange the equation into y = mx + b form. The equation becomes y = -8x + 6. The slope is -8, not 8. So, this equation does not represent a line that is perpendicular to the given line.
B. x - 8y = 40: Rearranging the equation into y = mx + b form, we get -8y = -x + 40, which simplifies to y = 1/8x - 5. The slope is 1/8, not 8. So, this equation does not represent a line that is perpendicular to the given line.
C. x + 8y = 40: Rearranging the equation into y = mx + b form, we get y = -1/8x + 5. The slope is -1/8, not 8. So, this equation does not represent a line that is perpendicular to the given line.
D. y - 8x = -2: Rearranging the equation into y = mx + b form, we get y = 8x - 2. The slope is 8, which is the negative reciprocal of -1/8. Therefore, this equation represents a line that is perpendicular to the given line.
Therefore, the equation that represents a line perpendicular to the line y = -1/8x + 3 is D. y - 8x = -2.