Answer:
y = [tex]\frac{-x}{6} + \frac{28}{6}[/tex]
Step-by-step explanation:
First, we must find the slope of the current equation.
This is the number in front of the x.
Seeing as this is 6x, the slope of this line is 6
When finding the slope of a line perpendicular, you need to find the [tex]\frac{-1}{slope}[/tex]
So, in this case it is:
[tex]\frac{-1}{6}[/tex]
The negatives cancel out which leave [tex]\frac{1}{2}[/tex]
So the gradient is [tex]\frac{1}{2}[/tex]
Now, to find the equation of a line, you need to use:
y - y1 = m(x - x1)
Where y1 and x1 are the values in the coordinates (-6 , 4)
So y1 = 4, x1 = -6, and m is [tex]\frac{-1}{6}[/tex]. Plug these values in:
y - 4 = [tex]\frac{-1}{6}(x - -6)[/tex]
We need to get rid of the fraction so we multiply the whole equation by 6 (6 * 1/6 = 1):
6y - 24 = - (x - 2)
The minus outside the bracket means that every value inside the bracket is oposite:
6y - 24 = -x + 2
And now simply move the -24 over to the other side, making it a positive:
6y = -x +2 + 26
Simplify:
6y = -x + 28
Divide all values by 6 to get y:
y = [tex]\frac{-x}{6} + \frac{28}{6}[/tex]
So the equation of the line is y = [tex]\frac{-x}{6} + \frac{28}{6}[/tex]
