Determine which two equations represent parallel lines?

Question

(a) y = 5x – 7 (b) y = –5x + 7 (c) y = 5x + 3 (d) y = x – 7

Answer 1

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Answer 2

Parallel lines have the same slope, right? The slope is "m" in the generalized line equation "y = mx + b". So look for the two lines which have the same coefficients for x and y and it's obvious which two are parallel.

If you're a masochist, you can determine which pair of equations do not have a simultaneous solution. Non-parallel lines meet at a single point, so you can solve, say, the simultaneous equations (a) and (b) together above, and see that they intersect at [1.4, 0]. Doing this pairwise {e.g., solve (a) and (c), solve (a) and (d), solve (b) and (c), solve (b) and (d), and solve (c) and (d)} shows that one of these pairs of equations has no solution, while all the others do have one. Clearly, that's a lot more work and no fun unless you have to do it anyway, for example because your teacher is a sadist and has assigned you to find the intersections for all the non-parallel lines!

Answer 3

If two line parralel they have same gradient value

m1=m2

hence

general equation ; y=mx+c

hence

y=5x-7 parallel with y=5x+3

Answer 4

Parallel lines have the same slope. The slope is just the coefficient of x when the equation is in the form: y = mx +b. so......(a) and(c) both have m=5 so they are parallel.

Answer 5

Parallel lines have the same slope. Since these lines are in y = m x + b form already, this should be easy to see which have the same slope (m).

Answer 6

Parallel lines have the same slope. Which two have the same slope?