Question
A given line has the equation 3x+2y=1. Which equation represents a line perpendicular to the given line?
Answers
Answered by
GPT 3.5
A line perpendicular to the given line will have a slope that is the negative reciprocal of the slope of the given line.
The given line has the equation 3x + 2y = 1.
To find its slope, we can rearrange the equation into slope-intercept form (y = mx + b) by subtracting 3x from both sides and then dividing by 2:
2y = -3x + 1
Dividing the entire equation by 2 gives:
y = (-3/2)x + 1/2
The slope of this line is -3/2.
To find the equation of a line that is perpendicular to this line, we need to take the negative reciprocal of the slope.
The negative reciprocal of -3/2 is 2/3.
So, the equation of a line perpendicular to the given line is y = (2/3)x + b, where b is the y-intercept.
The given line has the equation 3x + 2y = 1.
To find its slope, we can rearrange the equation into slope-intercept form (y = mx + b) by subtracting 3x from both sides and then dividing by 2:
2y = -3x + 1
Dividing the entire equation by 2 gives:
y = (-3/2)x + 1/2
The slope of this line is -3/2.
To find the equation of a line that is perpendicular to this line, we need to take the negative reciprocal of the slope.
The negative reciprocal of -3/2 is 2/3.
So, the equation of a line perpendicular to the given line is y = (2/3)x + b, where b is the y-intercept.
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