Quick help on geometry please

[jordan7]

How do you find x in this example:
"If the line through (x,5) and (4,3) is parallel to a line with slope 3, find x."
I initially used the formula for slope of a line (m=Ysub2-Ysub1/Xsub2-Xsub1) to find the missing x. But what's throwing me off is the "parallel to a line" one.

Is my problem just same with, for example, find the x if the line through points (6,x) and (1,5) has a slope of 2?

And what difference would there be if it was perpendicular instead of parallel. I just need help in understanding thank you!

 

[pka]

Can you solve \(\dfrac{(3-5)}{(4-x)}=3~?\)

 

[jordan7]

(4-x)[(3-5)/(4-x)] = 3(4-x)

-2 = 12-3x
-3x = -2-12
-3x = -14
x = 14/3

I'm sorry if I write a little weird or I don't know how to use fractions in this format but I hope my solution was understandable/correct.

 

[Dr.Peterson]

How do you find x in this example:
"If the line through (x,5) and (4,3) is parallel to a line with slope 3, find x."
I initially used the formula for slope of a line (m=Ysub2-Ysub1/Xsub2-Xsub1) to find the missing x. But what's throwing me off is the "parallel to a line" one.

Is my problem just same with, for example, find the x if the line through points (6,x) and (1,5) has a slope of 2?

And what difference would there be if it was perpendicular instead of parallel. I just need help in understanding thank you!

Two lines are parallel if they have the same slope. So it's saying your line has slope 3.

Two lines are perpendicular if their slopes are negative reciprocals; so they'd be saying your line has slope -1/3.

 

[Deleted member 4993]

How do you find x in this example:
"If the line through (x,5) and (4,3) is parallel to a line with slope 3, find x."
I initially used the formula for slope of a line (m=Ysub2-Ysub1/Xsub2-Xsub1) to find the missing x. But what's throwing me off is the "parallel to a line" one.

Is my problem just same with, for example, find the x if the line through points (6,x) and (1,5) has a slope of 2?

And what difference would there be if it was perpendicular instead of parallel. I just need help in understanding thank you!

You say "what's throwing me off is the "parallel to a line" one."

When two lines, with slopes m₁ and m₂, are parallel then →​

​

m₁ = m₂​

And what difference would there be if it was perpendicular instead of parallel.

When two lines, with slopes m₁ and m₂, are perpendicular then →​

m₁ * m₂ = -1​

 

[jordan7]

Oh wait. I understand now, tried to solve a few more and analyzed the equations that has been posted here. Thanks for the brief explanations, it helped me more than I thought.