A line is perpendicular to y=x/4-2 and intersects at the point (4, -1) what is the equation of this perpendicular line

Answer 1

y=x/4 -2 has slope = 1/4, the coefficient of the x term, when a linear equation is solved for y

a perpendicular line has a negative inverse slope =-4/1 =-4

just flip the 1/4 fraction upside down and change its sign

the perpendicular line is

y = -4x + b

to find b, plug in the point (x,y) = (4,-1)

-1 = -4(4) +b

b = -1 +16 =15

y = -4x +15 in slope intercept form

4x+y = 15 in standard form

4x+y-15 = 0 in general form

if you want to know the distance from the given point to the original line

find where the two perpendicular lines intersect, set them equal

-4/x +15 = x/4 -2

5/x = 17

x = 5/17

y = -4(5/17) +15 = -20/17 + 15(17)/17 = 255-20/17 = 235/17 = 13 14/17

the point (5/17, 235/17)

then use the distance formula to find the distance from the intersection point to the given original point

Answer 2

A line is perpendicular to y=x/4-2 and intersects at the point (4, -1) what is the equation of this perpendicular line

We start with the equation y = x/4 - 2, which can be rewritten as y = 1/4 x - 2

This means the slope of this line is 1/4.

To find the slope of the line that is perpendicular to this line, we take the opposite reciprocal of 1/4, which is -4.

So m = -4, and we have the point (4,-1). We can plug these values into the point slope equation of a linear function, y-y1=m(x-x1).

y-(-1) = -4 (x-4)

y+1 = -4 (x-4) point slope form

y+1 = -4x+16

y= -4x +15 slope intercept form

4x+y=15 standard form

Answer 3

If the lines are perpendicular, their slopes are negative reciprocal. You can now use the point-slope form of an equation of line, plug the given point and the slope of the perpendicular line and find the equation of the line.

Answer 4