Answer:
1) y=1/5x +0.8
2) y= -2x +10
Step-by-step explanation:
It's been a while, but I think this is right:
1)
For 2 lines to be parallel they must have the same slope
Recall that the equation of a line is
y-y1 = m (x- x1)
m being slope
So looking at equation 1, we can tell that the slope is 1/5 because it has already been distributed to the x.
So we know our equation will look something like this
y-y1 = 1/5 (x- x1)
We also know that the line passes through the point (8,1)
So, you plug in those points to your equation
y- 1 = 1/5(x - 8)
Simplifying and distributing the equation, we end up with
y= 1/5x + 0.8
(if you would like me to explain the simplification plz ask in a comment.)
2)
First you have to move -x from the left side of the equation to the right, making the equation
2y= x+10
then divide by 2 on both sides (im writing x/2 as 1/2x, because they are the same)
y= 1/2x + 5
For 2 lines to be perpendicular they must have the opposite reciprocal slope
Meaning if you had a slope of 2, the opposite would be -2 and the reciprocal would be 1/2, so your slope would be -1/2
Knowing this and keeping in mind our equation of a line from the first question, our slope of a perpendicular line (or m in our equation) of y= 1/2x + 5
would be -2
So far we have an equation that looks like
y-y1 = -2 (x- x1)
So now we plug in our points (6, -2)
(y- -2)
y + 2 = -2 (x - 6)
Simplifying and distributing the equation, we end up with
y= -2x +10
(if you would like me to explain the simplification or have a question don't hesitate to ask in a comment.)
