pls help asap?

First, to compare two linear equations, they should both be in the form of
y = mx + b, called the "slope-intercept" format,
where
m = the slope of the line
b = the point where the line intersects (or intercepts) the y-axis (or x = 0)

1. y = 2x + 5 and y = 2x – 1

Both equations are in the point-slope format. Since m = 2 in both equations,
we know that they have the same slope and are therefore parallel.

2. y = x + 4 and x - 3y = - 12

The second equation needs to be changed into the y = mx + b format.
x - 3y = -12
-3y = -x - 12
-3y/-3 = -x/-3 - 12/-3
y = x/3 + 4
y = (1/3)x + 4

The two both have positive slopes, but since they are different slopes they
are not parallel. However, since the have the same y-intercept point, they
intersect at the point (0, 4).

3. y = 5x – 2 and x + 4y = 8

The second equation needs to be changed into the y = mx + b format.
x + 4y = 8
4y = -x + 8
4y/4 = -x/4 + 8/4
y = (-1/4)x + 2

The first equation has a positive slope, while the second equation has a
negative slope. To find their intersection point, do the following:

Set the slope-intercept equations as equal to each other.

5x - 2 = (-1/4)x + 2
5x - 2 = -0.25x + 2
5.25x - 2 = 2
5.25x = 2 + 2
5.25x = 4
5.25x/5.25 = 4/5.25
x = 0.761904762

Insert the above x-value into the first equation to get the y-coordinate of the
two lines' intersection point.

y = 5x – 2
y = 5(0.761905) - 2
y = 3.809524 - 2
y = 1.809524

So, the two lines' point of intersection is (0.76, 1.81).

1.
y = mx + c
where m is the slope and c is the y-intercept.

y = 2x + 5 …… [1]
y = 2x - 1 …… [2]

The two lines have the same slope, but different y-intercept.
PARALLEL

====
2.
y = x + 4 …… [1]
x - 3y = -12 …… [2]

Rewrite [2] as:
3y = x + 12
y = (1/3)x + 4 …… [2*]

The two lines have different slopes.
INTERSECT

====
3.
y = 5x - 2 …… [1]
x + 4y = 8 …… [2]

Rewrite [2] as:
4y = x - 8
y = (1/4)x - 2 …… [3]

The two lines have different slopes.
INTERSECT
(Point of intersection = (0, -2))

The equation of line to be in slope intercept form ..y=mx+b


1. y = 2x + 5 , y = 2x – 1 
slope of both lines is 2, so they are parallel

2. y = x + 4 , x - 3y = - 12
x - 3y = - 12 can be written as y = ⅓x + 4
Both lines have different slopes so they intercept

3. y = 5x – 2 , x + 4y = 8 
x + 4y = 8 can be written as y=-¼x + 2
Both lines have different slopes so they intercept

1. Parallel because the 'x' coefficient is the same.
2. y = x + 4 & y = x/3 + 4 They intersect at y = 4 , where the lines intersect the y- axis.
3. y = 5x - 2 & y = -x/4 + 2 Neither intersect nor parallel.