Answer:
Step-by-step 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.
