Which is the equation of a line that is perpendicular to the line with equation 3 x plus y equals 10? Answer options with 5 options A. y equals negative 3 x plus 10 B. y equals negative 1-third x plus 5 C. y equals 3 x minus 1-tenth D. y equals 3-tenths x plus 17 E. y equals 1-third x plus 20
Question
Which is the equation of a line that is perpendicular to the line with equation 3 x plus y equals 10?
Answer options with 5 options A. y equals negative 3 x plus 10
B. y equals negative 1-third x plus 5
C. y equals 3 x minus 1-tenth
D. y equals 3-tenths x plus 17
E. y equals 1-third x plus 20
Solution
The equation of the line given is 3x + y = 10.
First, we need to find the slope of this line. We can do this by rearranging the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Subtract 3x from both sides of the equation to get y = -3x + 10.
So, the slope of the given line is -3.
A line is perpendicular to another if the product of their slopes is -1.
Therefore, the slope of the line perpendicular to the given line is the negative reciprocal of -3, which is 1/3.
Looking at the answer choices, the line with a slope of 1/3 is:
E. y equals 1-third x plus 20.
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