Answer:
y = -6x - 24
Explanation:
Relationship between the slopes of perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other, as shown by the formula m2 = -1/m1, where
- m1 is the slope of the line we're given,
- and m2 is the slope of the line we're trying to find.
Identifying the form of x - 6y = -2
x - 6y = -2 is in the general form of a line, whose general equation is given by:
Ax + By = C, where
- A, B, and C are constants.
We can find the slope of this line by putting it in slope-intercept form.
General equation of the slope-intercept form and identifying the slope of x - 6y = -2:
The general equation of the slope-intercept form is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Thus, we can convert x - 6y = -2 to slope-intercept form and identify its slope by isolating y:
(x - 6y = -2) - x
(-6y = -x - 2) / -6
y = 1/6x + 1/3
Thus, the slope of x - 6y = - 2 (i.e., m1 in the perpendicular slope equation) is 1/6.
Finding the slope of the other line (i.e., m2 in the perpendicular slope formula):
Now we can find the slope of the other line by substituting 1/6 for m1 in the perpendicular slope formula:
m2 = -1 / (1/6)
m2 = -1 * 6
m2 = -6
Thus, the slope of the other line is -6.
Finding the y-intercept of the other line (b) and writing the equation of the line:
Now we can find the y-intercept (b) of the other line by substituting -6 for m and (-5, 6) for (x, y) in the slope-intercept form:
6 = -6(-5) + b
(6 = 30 + b) - 30
-24 = b
Thus, the y-intercept of the other line is -24.
Therefore, y = -6x - 24 is an equation of the line (in slope-intercept form) that passes through the given point (-5, 6) and is perpendicular to the line x - 6y = -2.