Which equation represents the line that is perpendicular to y equals 5 x plus 4 and passes through the point negative 5 comma 2?
The given equation is y = 5x + 4.
The equation of the line perpendicular to this line will have a slope that is the negative reciprocal of 5, which is -1/5.
Using the point-slope form y - y1 = m(x - x1) and the point (-5, 2), we have:
y - 2 = -1/5(x - (-5))
y - 2 = -1/5(x + 5)
y - 2 = -1/5x - 1
Rearranging the equation:
y = -1/5x + 1
Therefore, the equation of the line that is perpendicular to y = 5x + 4 and passes through the point (-5, 2) is y = -1/5x + 1.
the answer choices are
y = -1/5x + 1
y= -1/5x + 3
y= 5x - 23
y = 5x + 27
Based on the previous calculations, the correct equation that represents the line perpendicular to y = 5x + 4 and passes through the point (-5, 2) is:
y = -1/5x + 1
Among the answer choices, the equation that matches this result is y = -1/5x + 1.