Question

Question

Two lines in the coordinate plane have opposite slopes, are parallel, and the sum of their y-intercepts
is 11. If one of the lines passes through (7,3), what are the equations of the lines?
and
The equations of the lines are
slopes are opposites, the slopes must be
equation
; parallel lines have (select) v slopes, so if the
a line with this slope and passing through (7,3) has

Answer 1

Two lines in the coordinate plane have opposite slopes, are parallel, and the sum of their y-intercepts is 12. If one of the lines passes through (1, 8), what are the equations of the lines?

Explanation:

Answer 2

The equations of the lines are y=3 and y=8.

Parallel lines have equal slopes, so if the slopes are opposites, the slopes must be 0.

A line with this slope and passing through (7, 3) has equation y=3.

Explanation:

The above answer statements pretty much speak for themselves. The only opposite numbers that are equal are 0 and -0 = 0, so the slopes must be 0.

A line with a zero slope has a constant y-value, so is of the form ...

y = constant

If it goes through a point with a y-coordinate of 3, then the constant must be 3. The line is ...

y = 3

___

If the sum of two numbers is 11 and one of them is 3, the other is 8. So, the parallel line has equation y = 8.