Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation.

Question

(0, –5); x – 6y = –2

Answer 1

The equation  x – 6y = –2  is given in Standard Form (Ax+By=C).  Now, ONCE AND FOREVER, convert this to slope-intercept form (y=mx+b) [that is, y=(-A/B)x + (C/B] and remember that:

    --  the slope is (-A/B)

    --  the y-intercept is (C/B)

 

For the line x-6y=-2, the slope is (-1/(-6)) = 1/6.

 

The slope of all perpendicular lines is the negative reciprocal [which is (-6)].  The equation of all perpendicular lines is:

    6x + y = D      [slope is (-6/1) and we need a point, like (0,-5) to determine D]

    0 + (-5) = D

      -5 = D

 

In Standard Form, the equation of the perpendicular line is :   6x + y = -5

  If you want this in slope-intercept form:   y = -6x-5

Answer 2

Hi Aim,

To solve this problem, first we'll want the equation of the line to be in standard (y=mx+b) form. In this form, we know m will be equal to the slope and b will be equal to the y-intercept.
x-6y=-2

-6y=-x-2

y=(1/6)x+(1/3)

For the second line to be perpendicular to this one, it's slope (m in standard form) must be the negative reciprocal. To do this, simply flip the numerator and denominator and make it negative.

Negative Reciprocal of (1/6) = -(6/1) = -6
So the slope of the perpendicular line must be -6

y=(-6)x+b
To solve for our y-intercept, b, we just plug in the x and y values of the point the line must pass through (0,-5) and solve for b

 

-5=(-6)(0)+b

-5=0+b

-5=b

 

So the y-intercept (b) of our perpendicular line will be -5

Adding this to our last equation, the solution will be:

 

y=-6x-5