Question
Consider the line y=-5x+3
Find the equation of the line that is perpendicular to this line and passes through the point (-7,2).
Find the equation of the line that is parallel to this line and passes through the point (-7,2)
Find the equation of the line that is perpendicular to this line and passes through the point (-7,2).
Find the equation of the line that is parallel to this line and passes through the point (-7,2)
Answers
Answered by
GPT 3.5
To find the equation of the line that is perpendicular to y=-5x+3 and passes through the point (-7,2), we first need to determine the slope of the perpendicular line. The slope of a line perpendicular to a line with slope m is the negative reciprocal of m.
The slope of the line y=-5x+3 is -5. Therefore, the slope of the perpendicular line is the negative reciprocal of -5, which is 1/5.
Using the point-slope form of the equation of a line, the equation of the perpendicular line passing through (-7,2) is:
y - 2 = 1/5(x + 7)
y - 2 = 1/5x + 7/5
y = 1/5x + 7/5 + 2
y = 1/5x + 17/5
Therefore, the equation of the line that is perpendicular to y=-5x+3 and passes through the point (-7,2) is y = 1/5x + 17/5.
To find the equation of the line that is parallel to y=-5x+3 and passes through the point (-7,2), we can use the fact that parallel lines have the same slope.
Since the slope of the line y=-5x+3 is -5, the slope of the parallel line is also -5. Using the point-slope form of the equation of a line, the equation of the parallel line passing through (-7,2) is:
y - 2 = -5(x + 7)
y - 2 = -5x - 35
y = -5x - 33
Therefore, the equation of the line that is parallel to y=-5x+3 and passes through the point (-7,2) is y = -5x - 33.
The slope of the line y=-5x+3 is -5. Therefore, the slope of the perpendicular line is the negative reciprocal of -5, which is 1/5.
Using the point-slope form of the equation of a line, the equation of the perpendicular line passing through (-7,2) is:
y - 2 = 1/5(x + 7)
y - 2 = 1/5x + 7/5
y = 1/5x + 7/5 + 2
y = 1/5x + 17/5
Therefore, the equation of the line that is perpendicular to y=-5x+3 and passes through the point (-7,2) is y = 1/5x + 17/5.
To find the equation of the line that is parallel to y=-5x+3 and passes through the point (-7,2), we can use the fact that parallel lines have the same slope.
Since the slope of the line y=-5x+3 is -5, the slope of the parallel line is also -5. Using the point-slope form of the equation of a line, the equation of the parallel line passing through (-7,2) is:
y - 2 = -5(x + 7)
y - 2 = -5x - 35
y = -5x - 33
Therefore, the equation of the line that is parallel to y=-5x+3 and passes through the point (-7,2) is y = -5x - 33.