Question

4

Which of the following equations defines a line that is parallel to the line y = -x - 4 and
asses through the point (3,-1)?
O A
OB
0 c
D
y =
y =
-
-
4
-x-1
43
4
--X
-
3
4
y=-3x+1
4
y = -x +3

Answer 1

To find an equation of a line that is parallel to the line y = -x - 4 and passes through the point (3, -1), we can use the fact that parallel lines have the same slope. The given line has a slope of -1, so any line parallel to it must also have a slope of -1.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values (3, -1) for (x1, y1) and -1 for m, we get:

y - (-1) = -1(x - 3)

y + 1 = -x + 3

y = -x + 2

Therefore, the equation of a line that is parallel to y = -x - 4 and passes through the point (3, -1) is y = -x + 2.

Explanation: