Math question?

Question

please explain i don't get this at all step by step
1.is parallel to the line through (4,-3)and (-2,1) and contains (0,0)
2.is perpendicular to the x- axis and passes through(1,4)

Answer 1

1.the slope if the line is the change in y over the change in x, so the slope is (-3-1)/(4- -2), and so the slope is -2/6, or -1/3, and so the equation so far is y=-1/3x+b
since the line contains (0,0) the y intercept, or b, must equal 0, so the line equation is y=-1/3x

2. the line has no equation, since the line perpendicular to the x axis has an indefinate slope. if you were to write an equation, it would be x=1

Answer 2

From 1 you can find the slope of the line your looking for:
difference in y's / difference in x's
then you use the point slope formula to find your line:
y=slope*(x-x coordinate)+y coordinate
Since the 2 coordinates your given are 0,0 it just looks like this
y=slope*x
2. "Is perpendicular to the x axis" means it is a verticle line, or the slope is equal to infinity. in this case the only number that matters is the x coordinate (1). The line is x=1. This is because a vertical line drawn through x=1 will give every set of coordinates (1, any other number).

Answer 3

1 equation of the line through (4,-3)and (-2,1) is
a = (y1 - y2 ) / (x1 - x2) = -4 /6 = -2/3
b = y1 - a x1
the parallel that contains 0 has the same director coefficient so
y= -2/3 x
2 x axis is y = 0 and orthogonal is x= 0
it pass through (1,4) so it is x = 1

Answer 4

1.
a)(4.-3); b) (2,-1)

(y - ya)(xb-xa)= (x- xa)(yb-ya)
(y -(-3))(2-4)=(x-4)(-1-(-3))
-2y -6= 2x -8
-y -3= x-4
y= -x +1