Answer:
b. 5x - y = 6 and 2x + 10y = 22
Explanation:
When two lines are perpendicular, their slopes are negative reciprocals as shown by the following formula:
m2 = -1 / m1, where
- m2 is the slope of one line,
- and m1 is the slope of the other line.
Currently, 5x - y = 6 and 2x + 10y = 22 are in standard form whose general equation is:
Ax + By = C.
In order to determine the slopes of both lines, we can convert both lines to slope-intercept form, whose general equation is:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Converting 5x - y = 6 to slope-intercept form:
(5x - y = 6) - 5x
(-y = -5x + 6) / -1
y = 5x - 6
Thus, the slope of 5x - y = 6 is 5.
Converting 2x + 10y = 22 to slope-intercept form:
(2x + 10y = 22) - 2x
(10y = -2x + 22) / 10
y = -1/5x + 11/5
Thus, the slope of 2x + 10y = 22 is -1/5.
Checking that the slopes are negative reciprocal:
To check that the slopes are negative reciprocals by plugging in both 5 and -1/5 for m1 in the perpendicular slope formula and checking that we get 5 and -1/5 respectively:
Checking 5 for m1:
m2 = -1 / 5
m2 = -1/5
Checking -1/5 for m1:
m2 = -1 / (-1/5)
m2 = -1 * -5/1
m2 = 5
Thus, the two slopes are negative reciprocals, and thus 5x - y = 6 and 2x + 10y = 22 are perpendicular.