Answer:
Neither
Explanation:
Relationship of slopes with parallel and perpendicular lines:
Parallel lines:
- The slopes of parallel lines have the same slope.
Perpendicular lines:
- The slopes of perpendicular lines are negative reciprocals of each other.
This is shown by the formula m2 = -1 / m1, where
- m2 is the slope of one line,
- and m2 is the slope of the other line.
Identifying the forms of 2x + 3y - 6 = 0 and -6x + 9y + 10 = 0:
Both 2x + 3y - 6 = 0 and -6x + 9y + 10 = 0 are in the general form of a line, whose general equation is given by:
Ax + By + C = 0, where
- A, B, and C are constants.
Determining the slopes of 2x + 3y - 6 = 0 and -6x + 9y + 10 = 0:
The easiest way to identify the slope is to convert form general from to slope-intercept form, whose general equation is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Converting from general form to slope-intercept form:
Thus, we can convert form general form to slope-intercept form by isolating y on the left-hand side:
Converting 2x + 3y - 6 = 0 to slope-intercept form:
(2x + 3y - 6 = 0) - 2x + 6
(3y = -2x + 6) / 3
y = -2/3x + 2
Converting -6x + 9y + 10 = 0 to slope-intercept form:
(-6x + 9y + 10 = 0) + 6x - 10
(9y = 6x - 10) / 9
y = 2/3x - 10/9
Since the slopes are not the same nor are they negative reciprocals of each other, the lines are neither parallel nor perpendicular.