Question

Which two lines are parallel? How do you know?

A. 2x-y=52x−y=5
B. 2x+y=32x+y=3
C. y=2x+3y=2x+3

Answer 1

Lines A (2x - y = 5) and C (y = 2x + 3) are parallel because, after rearranging into slope-intercept form, they both have the same slope of 2.

Step-by-step explanation:

The subject in question is linear equations which falls under the category of Mathematics, specifically within algebra. To determine which lines are parallel, one must look at the slope of each line. In the provided equations, we can rearrange them into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Let's rewrite each equation:

• A: 2x - y = 5 can be rewritten as y = 2x - 5, thus the slope (m) is 2.
• B: 2x + y = 3 can be rewritten as y = -2x + 3, thus the slope (m) is -2.
• C: y = 2x + 3 already has the slope of 2 in slope-intercept form.

Since lines with the same slope are parallel, equations A and C are parallel because they both have a slope of 2. Equations B has a different slope and therefore is not parallel to A or C.