Question

Consider the line y=3x-3.

Find the equation of the line that is parallel to this line and passes through the point (-8,6).

Find the equation of the line that is perpendicular to this line and passes through the point (-8,6)


Equation of parallel line: ?

Equation of perpendicular line: ?

Answer 1

I have no idea how to solve it?!

Answer 2

i wish any buddy can help solve it

Answer 3

Yes I can help you.

Answer 4

Consider the line y=3x-3. Find the equation of the line that is parallel to this line and passes through the point (-8,6).

ans: if a line is parallel, then that means both the lines have the same gradient. in this case y=mx+c .. the gradient is m. m=3.
now take that information and plug it into this equation to create an equation
y-y1=m(x-x1) where
y1 is 6
m=3
x1=-8

y-6=3(x--8)
y-6=3(x+8)
Expand
y-6=3x+24
plus 6 to both sides
y=3x+30
therefore. 3x+30 is a line parallel to the line y=3x-3 going through (-8,6)

Answer 5

thank you so much this is so helpful i understood it, so the parallel line is y=3x+30, how about the perpendicular line whats going to be the answer for it.

Answer 6

Consider the line y=3x-3.Find the equation of the line that is perpendicular to this line and passes through the point (-8,6)

ans: if a line is perpendicular, then multiplying both their gradients will result to -1
as mentioned before the gradient of y=3x-3 is m=3

m1 * m2= -1
where m1 is gradient of original line y=3x-3 and m2 is the gradient of the perpendicular line going thorough (-8,6) - which we dont know yet. but we can solve for it

m1 * m2 = -1
3 * m2 = -1
m2 =-1/3

so now we have the gradient of the perpendicular line which is -1/3

so now plug this information into the equation y-y1=m(x-x1) to obtain our equation
gradient= -1/3
x1= -8
y1=6
y-y1=m(x-x1)
y-6=-1/3(x--8)
y-6=-1/3(x+8)
y-6=-1/3x-8/3
\[y=\frac{ -1 }{ 3 }x+\frac{ 10 }{ 3 }\]

Answer 7

aha! now i got it.

Answer 8

thanks! :) sorry i got carried away doing the maths (lol sometimes i get all excited doing the maths to get the answer) haha

Answer 9

actually thanks to you for all what you have done. you made it simple to me