Question

Segment AB falls on line 6x + 3y = 12. Segment CD falls on line 4x+2y=8. What is true about segments AB and CD?

O They are parallel because they have the same slope of -2.
O They are parallel because they have the same slope of
2
O They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.
O They are lines that lie exactly on top of one another because they have the same slope and a different y-intercept

Answer 1

(c) They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

Explanation:

You want to know the relation between the lines ...

• 6x +3y = 12
• 4x +2y = 8

Standard form

These equations can be put into standard form by removing the common factor from the coefficients:

• 6x +3y = 12 ÷3 ⇒ 2x +y = 4
• 4x +2y = 8 ÷2 ⇒ 2x +y = 4

We see that the equations give the same line. That is ...

(c) They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

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