Question

Which pair of the following straight lines are parallel and how?

a. 2x + y + 1 = 0
b. y = 3x - 1
c. 2x - y = 3
d. y = 4x + 3
e. y = x/2 - 1
f. 6x - 2y = 0
g. 3y = x + 4
h. 2y = 5 - x

Answer 1

Explanation:

assuming you know how to put the equations into y = m x + b already. All equations have to be put in that format to identify the slope. Parallel lines have the same slope.

a. y = -2x - 1; slope -2

b. y = 3x - 1; slope 3

c. y = 2x - 3; slope 2

d. y = 4x + 3; slope 4

e. y = x/2 - 1; slope 1/2

f. y = 3x; slope 3

g. y = x/3 + 4/3; slope 1/3

h. y = -x/2 + 5; slope -1/2

There are only 2 that are alike. b and f both have a slope of 3. all the other slopes are different.

Answer 2

f and b

Explanation:

if you put them in y-intercept form, both slopes are 3

In b. it's easy to see that 3x has a slope of 3.

In f. it's not so obvious. Just solve for y or use the shortcut m = -a/b where a is the coefficient of x and b is the coeff of y.

hence -(6/-2)=3