Respuesta :
Answer:
The correct option is 2.
Step-by-step explanation:
The slope of two parallel lines are equal.
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
In option 1, the equation of lines are
[tex]y=9[/tex]
[tex]x=18[/tex]
The first line is a horizontal line and the second line is a vertical line. Therefore they are not parallel line. Option 1 is incorrect.
In option 2, the equation of lines are
[tex]y=4x+9[/tex]
[tex]y=4x-9[/tex]
By using the slope intercept form of a line, the slope of first line is 4 and the slope of second line is 4.
Since the slope of both lines are same, therefore both lines are parallel. Option 2 is correct.
In option 2, the equation of lines are
[tex]y=5x+15[/tex]
[tex]y=-5x+15[/tex]
By using the slope intercept form of a line, the slope of first line is 5 and the slope of second line is -5.
Since the slope of both lines are not same, therefore both lines are not parallel. Option 3 is incorrect.
Answer:
Option B.
Step-by-step explanation:
If two lines are in the form of y = mx + c and y' = m'x' + c'
and the given lines are parallel then their slopes will be same.
For this condition m = m'
Now we will analyse each option for the condition that the given lines are parallel lines.
Option A. y = 9 and x = 18
These lines are horizontal and vertical lines so they are not parallel.
Option B. y = 4x + 9 and y = 4x - 9
y = 4x + 9 slope of the line is m = 4
y = 4x - 9 slope of this line is m' = 4
Slopes are same so both the lines are parallel.
Option C. y = 5x + 15 and y = -5x + 15
for y = 5x + 15 slope m = 5
for y = -5x + 15 slope m' = -5
Slopes are not equal so the lines are not parallel.
Option B. is the answer.
