Given the equations of lines, which are parallel, perpendicular, concurrent?

Question

Identify if paralle, perpendicula, concurrent the following.

a) y=3x+3

b) y=3x-2

c) y=2x+4

d) 2y=4x+4

e) y=2/3x+3

f) y=-3/2x+3

g) 4x+3y=6

h) 4x+3y=8

Answer 1

Note :

1.If two lines are parallel, then they have the same slope and different y - intercepts.

2.To tell the two lines are perpendicular, the two lines in the same plane have slopes are negative reciprocals.

• a). y = 3x + 3.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = 3 and y - intercept b = 3.

b). y = 3x - 2.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = 3 and y - intercept b = - 2.

Therefore,a & b are parallel lines,because they have the same slope and different y - intercepts.

• c).y = 2x + 4.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = 2 and y - intercept b = 4.

d). 2y = 4x + 4.
Write the equation in slope intercept form

y = 2x + 2

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with y = mx + b.

slope m = 2 and y - intercept b = - 2.

Therefore,c & d are parallel lines,because they have the same slope and different y - intercepts.

• e).y = 2 / 3x + 3.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = 2 / 3 and y - intercept b = 3.

f). y = - 3 / 2x + 3.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with y = mx + b.

slope m = - 3 / 2 and y - intercept b = 3.

Therefore,e & f are perpendicular lines,because, the two lines in the same plane have slopes are negative reciprocals.

• g).4x + 3y = 6.

Write the equation in slope intercept form

y = - 4 / 3 (x ) + 2.

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = - 4 / 3 and y - intercept b = 2.

h). 4x + 3y = 8.

Write the equation in slope intercept form

y = - 4 / 3 (x ) + (8 / 3).

Slope intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Compare the above equation with  y = mx + b.

slope m = - 4 / 3 and y - intercept b = 8 / 3.

Therefore,g & h are parallel lines,because they have the same slope and different y - intercepts.