Equation of a line given, [tex] y=5x-5 [/tex]
If the general equation is [tex] y = mx+c [/tex]
The slope of the equation is m.
Here in the given equation the value of m is 5, so slope of the equation is 5.
To find the equation which is perpendicular to the given equation, the slope will be negative reciprocal of the slope of the given equation.
So the slope of the perpendicular equation = -1/5
We can write the perpendicular equation as [tex] y= (-1/5)x+c [/tex]
This equation passes through the point (-6,-6).
We will have to plug in x = -6 and y = -6 to the equation to get the value of c.
[tex] y = (-1/5)x+c [/tex]
[tex] -6 = (-1/5)(-6) + c [/tex]
[tex] -6 = (6/5) + c [/tex]
[tex] -6-6/5 = c [/tex]
[tex] -30/5 -6/5 = c [/tex]
[tex] -36/5 = c [/tex]
So we have got the value of c = -36/5
The equation of the perpendicular line is [tex] y = (-1/5)x - 36/5 [/tex]
Now to find the parallel line the slope is same as it is in the given equation. So the slope is 5 here.
So we can write the parallel equation as [tex] y = 5x+c [/tex]
The equation passes through the point (-6,-6).
If we plug in x = -6 and y=-6 in the given equation we will get,
[tex] y=5x+c [/tex]
[tex] -6= 5(-6)+c [/tex]
[tex] -6 = -30+c [/tex]
[tex] -6+30 = c [/tex]
[tex] 24 = c [/tex]
So we can write the parallel equation as [tex] y = 5x+24 [/tex]
So we have got the required answer.
The perpendicular equation is y = (-1/5)x - 36/5
And the parallel equation is y = 5x+24.
