Question
Write an equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x-8
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GPT 3.5
To find the equation of the line that passes through (-4,2) and is perpendicular to the line y = (2/7)x - 8, we first need to find the slope of the perpendicular line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of 2/7, so the perpendicular line will have a slope of -7/2.
Now that we have the slope of the perpendicular line, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is given by:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Plugging in the values of the slope and the point (-4,2), we get:
y - 2 = (-7/2)(x - (-4))
y - 2 = (-7/2)(x + 4)
y - 2 = (-7/2)x - 14
y = (-7/2)x - 12
Therefore, the equation of the line passing through (-4,2) and perpendicular to y = (2/7)x - 8 is y = (-7/2)x - 12.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of 2/7, so the perpendicular line will have a slope of -7/2.
Now that we have the slope of the perpendicular line, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is given by:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Plugging in the values of the slope and the point (-4,2), we get:
y - 2 = (-7/2)(x - (-4))
y - 2 = (-7/2)(x + 4)
y - 2 = (-7/2)x - 14
y = (-7/2)x - 12
Therefore, the equation of the line passing through (-4,2) and perpendicular to y = (2/7)x - 8 is y = (-7/2)x - 12.
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