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