Respuesta :
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 is in this form with slope m = 3
• Parallel lines have equal slope
• The slopes of perpendicular lines are negative reciprocals of each other
A
y = - [tex]\frac{1}{3}[/tex] x - 8 has slope m = - [tex]\frac{1}{3}[/tex]
3 and - [tex]\frac{1}{3}[/tex] are negative reciprocals
This line is perpendicular to y = 3x + 2
B
y = 3x - 10 has slope m = 3
This line is parallel to y = 3x + 2
C
y = 2x + 4 has slope m = 2
This line is neither parallel nor perpendicular to y = 3x + 2
The line which is parallel to the line [tex]y = 3x+2[/tex] is (y = 3x - 10) and the line which is perpendicular to the line [tex]y = 3x+2[/tex] is [tex]y =- \dfrac{1}{3}x-8[/tex] and can be determined by using the slope intercept form.
Given :
Equation - [tex]y = 3x+2[/tex]
First, find the slope of the line [tex]y = 3x+2[/tex].
m = 3
Now, consider each equation to determine which line is parallel or perpendicular to the line (y = 3x + 2).
A). [tex]y =- \dfrac{1}{3}x-8[/tex]
The slope of the equation [tex]y =- \dfrac{1}{3}x-8[/tex] is:
[tex]\rm m_1 = -\dfrac{1}{3}[/tex]
When the two lines are perpendicular to each other then their slopes are: [tex]\rm mm_1=-1[/tex]
[tex]\rm mm_1=-\dfrac{1}{3}\times 3=-1[/tex]
Therefore, the line [tex]y =- \dfrac{1}{3}x-8[/tex] is perpendicular to the line [tex]y = 3x+2[/tex].
B). y = 3x - 10
The slope of the equation y = 3x - 10 is:
[tex]\rm m_2 = 3[/tex]
When the two lines are parallel to each other then their slopes are same. Therefore, the line (y = 3x - 10) is parallel to the line [tex]y = 3x+2[/tex].
C). y = 2x + 4
The slope of the equation (y = 2x + 4) is:
[tex]m_3 = 2[/tex]
Therefore, the line (y = 2x + 4) is neither parallel nor perpendicular to the line [tex]y = 3x+2[/tex].
For more information, refer to the link given below:
https://brainly.com/question/11824567
