What is an equation of the line that passes through the point (-1,4) and is perpendicular to the line x-6y=12

6x + y = 3

Step-by-step explanation:

The product of two lines that are perpendicular to each other is -1

If line A has a slope of m1

and line B has a slope of m2 and they are perpendicular to each other,

then the product of the two lines is

m1 X m2 = -1

We are given two lines that are perpendicular to each other in the question.

The first line has the equation

x - 6y =12

We can write the slope form of the equation y = mx + c

m = slope

x - 6y = 12

Make y subject of formula

6y = x - 12

y = x/6 - 12/6

y = x/6 - 2

y =(1/6)x - 2

Comparing y=mx+c and y=(1/6)x-2,

m corresponds to 1/6

Therefore, we can say that the slope, m of the line x-6y=12

is 1/6

Recall, for two lines that are perpendicular to each other,

m1 X m2 = -1

m1 = 1/6

1/6 X m2 = -1

m2/6 = -1

Cross multiply

m2 = 6 X -1

m2 = -6

Step 3

To find the equation of the second line with slope, m2 = -6 and that passes through the point (-1,4)

Points are represented by coordinates (x, y)

the slope of a line is given by

m = (y - y1)/(x-x1)

Given in the question, the point (-1,4) corresponds to (x1, y1).

As calculated earlier, the slope of the second line is -6

-6 = (y - 4)/[x - (-1)]

-6 = (y - 4)/(x + 1)

Cross multiply

y - 4 = -6(x + 1)

y - 4 = -6x - 1

y = -6x - 1 + 4

y = -6x + 3

this equation is the slope form equation of the line

6x + y = 3 is the general form of the equation

To get from 60 to 100 you multiply by .6, so to get from 36 to what the first place would get you multiply by .6 and you get 60. Hopefully it helps!