What is the equation of the line perpendicular to #y=-2/21x # that passes through # (-1,6) #?

2 Answers
Mar 13, 2016

Answer:

The slope of a perpendicular line is the negative reciprocal of the original line.

Explanation:

The slope of the perpendicular line is #21/2#, since the original line has a slope of #-2/21#.

Now we can use point slope form to plug in the point, the slope abs find the slope intercept form equation.

#y - y_1 = m(x - x_1)#

The point (-1,6) is #(x_1, y_1)# while m is the slope.

#y - 6 = 21/2(x - (-1))#

#y - 6 = 21/2x + 21/2#

#y = 21/2x + 21/2 + 6#

#y = 21/2x + 33/2#

Hopefully this helps!

Mar 13, 2016

Answer:

#y=21/2x+33/2#

Explanation:

Given:#" "y=-2/21x# ..............................(1)

Compare to the standard form of#" " y= mx+c#

Where
#m# is the gradient
#x# is the independent variable (can take any value you wish)
#y# is the dependant variable. Its value depend on that of #x#
#c# is a constant that for a straight line graph is the y-intercept

In your equation #c=0# the #"y-intercept "-> y=0#

If #m# is the gradient of the given line then #-1/m# is the gradient of a line perpendicular to it.

#color(blue)("So for the perpendicular line")#

#" "y_("perp") = (-1)xx(-21/2)xx x + c#

#color(blue)(" "y_("perp") = +21/2x + c)#......................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the value of "c)#

We know that this new line passes through#(x,y)->(-1,6)#

So substitute into equation (2) the values #(x,y)->(color(green)(-1),color(magenta)(6))#

#" "y_("perp") =color(magenta)(6) = +21/2(color(green)(-1)) + c......................(2_a)#

#color(blue)(c=6+21/2 = 33/2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

The line perpendicular to that given is: #y=21/2x+33/2#

Tony B