Which of the following equations represents a line that is perpendicular to the line represented by
x
+
2
y
=
6
and passes through the point
(
3
,
−
4
)
?
A.
2
x
+
y
=
2
B.
x
+
2
y
=
11
C.
−
2
x
+
y
=
−
10
D.
−
2
x
+
y
=
7
To find the line that is perpendicular to the given line, we need to find the slope of the given line and then take the negative reciprocal to get the slope of the perpendicular line.
The given line is in standard form, so we need to rearrange it to slope-intercept form (y = mx + b) to find the slope.
x + 2y = 6
2y = -x + 6
y = -1/2x + 3
The slope of the given line is -1/2. The negative reciprocal of -1/2 is 2.
Now we have the slope (m = 2) and a point (3, -4) that the perpendicular line passes through. We can use the point-slope form of a linear equation to find the equation of the perpendicular line.
y - y1 = m(x - x1)
y - (-4) = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 10
None of the given equations match the equation of the perpendicular line, so the correct answer is not provided.