Explanation:
To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.
y = 5x – 2 is already in slope-intercept form, so its slope is 5.
These two slopes are not equal, so the lines are not parallel.
B) x + y = 0 can be rearranged to y = −x, so its slope is −1.
y = x + 7 is already in slope-intercept form, so its slope is 1.
These two slopes are not equal, so the lines are not parallel.
C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.
4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.
These two slopes are not equal, so the lines are not parallel.
D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.
y = 2x + 2 is already in slope-intercept form, so its slope is 2.
These two slopes are not equal, so the lines are not parallel.
E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.
y = 3x − 10 is already in slope-intercept form, so its slope is 3.
These two slopes are equal, so the lines are parallel.
Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.