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two lines in the coordinate plane has opposites slopes, are parallel, and the sum of theie y-intercepts is 12. if one of the lines passes through (2,3) what are equarions of the lines?

two lines in the coordinate plane has opposites slopes, are parallel, and the sum-example-1
User Aniket Sinha
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1 Answer

14 votes
14 votes

y = 3

y = 9

Step-by-step explanation:

For two lines to be parallel, their slope must be equal.

Now, we are told the lines have opposite slopes. This means the slopes are 0.

This because the slopes need to be the same and be opposite to each other.

The only number with this characteristic is 0.

The opposites are 0 and -0. Both are equal to zero.

The equation of line with slope zero, will have a constant y coordinate.

This because: y = mx + c

when m = 0, we will be left with:

y = c = y-intercept

GIven poin: (2, 3) = (x, y)

In our question, the y coordinate from the point given is 3

The equation of one the line: y = 3

we are told the sum of the y intercept of both lines = 12

since the first y-intercept = 3

1st y-intercept + 2nd y- intercept = 12

The second y-intercept = 12 - 3 = 9

slope of the second one is also 0, y = c = y-intercept

The equations of the line:

y = 3

y = 9

we complete the sentence:

The equations of the lines are y = 3 and y = 9; parallel lines have same slopes;

So if slopes are opposites, the slopes must be zero. A line with the slope and passing through (2, 3) has an equation y = 3

User Eduardo Vargas
by
3.0k points
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