Answer:
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
