What is the equation of the line perpendicular to #y=-1/5x # that passes through # (7,4) #?

Answer 1

Eli Assouline

#y=5x-31#

Given -

#y=-1/5x#

Slope of the given line

#m_1=-1/5#

The two line are perpendicular

Slope of the second line #m_2=1/(m_1) xx-1=-5 xx -1 =5#

Second line passes through the point #(7, 4)#

Equation of the second line

#y=mx+c#
#4=(5 xx 7)+c#
#4=35+c#
#c=4-35=-31#
#y=5x-31#

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Answer 2

Genesis Allen

The slope of a line perpendicular to (y = -\frac{1}{5}x) is the negative reciprocal of (-\frac{1}{5}), which is (5). The equation of a line in slope-intercept form is (y = mx + b), where (m) is the slope and (b) is the y-intercept.

Given the slope (5) and that the line passes through the point ((7,4)), we can substitute these values into the slope-intercept form to find (b):

[4 = 5(7) + b]

Solving for (b):

[4 = 35 + b] [b = 4 - 35] [b = -31]

Therefore, the equation of the line is:

[y = 5x - 31]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.