SOLUTION: How do I determine which two equations represent parallel lines? (a) y = 5/3x + 4 (b) y = 3/5x - 7 (c) y = 2x + 8 (d) y = 2x

SOLUTION: How do I determine which two equations represent parallel lines? (a) y = 5/3x + 4 (b) y = 3/5x - 7 (c) y = 2x + 8 (d) y = 2x - 4??

Question 120499: How do I determine which two equations represent parallel lines? (a) y = 5/3x + 4 (b) y = 3/5x - 7 (c) y = 2x + 8 (d) y = 2x - 4??
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
All of these equations are in the slope-intercept form. This form is:
.
y = m*x + b
.
where m ... the multiplier of x ... is the slope and b is the value on the y-axis where the
graph crosses the y-axis.
.
From this you can tell that the slope of the graph for equation (a) is (5/3) because (5/3)
is the multiplier of x.
.
Similarly the slope of (b) is (3/5)
.
The slope of (c) is 2
.
and the slope of (d) is 2
.
If the lines are to be parallel, they must have the same slopes. (You might be able to
visualize that if the slopes are different, the lines have to intersect at some place.)
.
Notice that equations (c) and (d) both have the same slope and therefore, they are the
pair of graphs that are parallel.
.
To help you visualize the graphs ... here they are. The graph of (a) is in "red" ... (b) is
in green ... (c) is in blue ... and (d) is in purple. You can see that the blue and purple
graphs (c) and (d) are parallel.
.

.
Hope this helps you to understand the problem.
.
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