What is the equation of the line perpendicular to #y - 4 = 0# and passing through (-1, 6)? Please show working.

Answer 1

#x=-1#

#"note that "y-4=0" can be expressed as "y=4#

#"This is a horizontal line parallel to the x-axis passing "# #"through all points in the plane with a y-coordinate "=4#

#"A line perpendicular to "y=4" must therefore be a "# #"vertical line parallel to the y-axis"#

#"such a line has equation "x=c" where c is the value"#

#"of the x-coordinate the line passes through"#

#"here the line passes through "(-1,6)#

#"the equation of the perpendicular line is therefore"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(x=-1)color(white)(2/2)|)))# graph{(y-0.001x-4)(y-1000x-1000)=0 [-10, 10, -5, 5]}

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Answer 2

Maverick Smith

To find the equation of the line perpendicular to $y - 4 = 0$ and passing through (-1, 6), we first need to find the slope of the given line. The equation $y - 4 = 0$ simplifies to $y = 4$ , indicating a horizontal line with a slope of 0.

Since the line we seek is perpendicular, its slope will be the negative reciprocal of the slope of the given line. The negative reciprocal of 0 is undefined, but in this case, since the original line is horizontal, the perpendicular line will be vertical.

Therefore, the equation of the perpendicular line passing through (-1, 6) is $x = -1$ .

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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.