Answer:
Slope of a parallel line = -1/4
Slope of a perpendicular line = 4
Explanation:
Relationship between the slopes of parallel lines:
- The slopes of parallel lines are the same.
We can show this with the formula m2 = m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we're given.
Relationship between the slopes of perpendicular lines:
- The slopes of perpendicular lines are negative reciprocals of each other.
We can show this with the formula m2 = -1/m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we're given.
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Step 1: Convert x + 4y = 6 to slope-intercept form:
x + 4y = 6 is in the standard form of a line, whose general equation is given by:
Ax + By = C, where
- A, B, and C are constants.
Given the standard form of a line, we can find the slope by converting it to slope-intercept form, whose general equation is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Thus, we need to isolate y to convert x + 4y = 6 to slope-intercept form:
(x + 4y = 6) - x
(4y = -x + 6) / 4
y = -1/4x + 3/2
Thus, the slope of x + 4y = 6 is -1/4.
Step 2: Find the slope of the line parallel to x + 4y = 6:
Since the slopes of parallel lines are the same, -1/4 is also the slope of the line parallel to x + 4y = 6.
Step 3: Find the slope of the line perpendicular to x + 4y = 6:
Since the slopes of perpendicular lines are negative reciprocals to each other and the slope of x + 4y = 6 is -1/4, we can plug in -1/4 for m1 to find m2, the slope of the other line:
m2 = -1 / (-1/4)
m2 = -1 * -4/1
m2 = 4
Thus, 4 is the slope of the line perpendicular to x + 4y = 6.