Question

Which two lines are parallel?

3x + y = -2 ***

2y – 6x = 4

2y = -6x – 8 **

how do I check if they're parallel????

Answer 1

• 3x + y = -2
• 2y = -6x – 8

Explanation:

When the equations are written in the same form, the ratio of x coefficient to y coefficient is the same for parallel lines.

These equations in the same form are ...

• 3x +y = -2
• -6x +2y = 4
• 6x +2y = -8

The first and last of these equations have a ratio of x-coefficient to y-coefficient of ...

(x-coefficient)/(y-coefficient) = 3/1 = 6/2

so the lines are parallel.

The second equation has a ratio that is the opposite of this.

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Alternate approach

You can put each equation into slope-intercept form (solve for y). The x-coefficient is then the slope of the line. Parallel lines** have equal slopes.

• y = -3x -2 **
• y = 3x +2
• y = -3x -4 **

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I find a graphing calculator to be a big help for many problems involving equations and their characteristics.