#1
What is the equation of the line parallel to y = 3x + 2?
y = 3x + 4
ExplanationParallel lines have the same slope; in this case, it remains 3, but the y-intercept shifts by 2 units.
#2
Which of the following pairs of equations represent parallel lines?
y = -3x + 2 and y = 3x + 5
ExplanationParallel lines have equal slopes; here, both have a slope of 3.
#3
What is the condition for two lines to be parallel in terms of their slopes?
Their slopes must be equal.
ExplanationFor lines to be parallel, their slopes must be identical.
#4
If the equation of a line is y = 4x - 3, what is the slope of a line parallel to it?
4
ExplanationParallel lines have the same slope; here, it remains 4.
#5
If the slopes of two lines are negative reciprocals of each other, what can be said about the relationship between these lines?
They are perpendicular.
ExplanationPerpendicular lines have slopes that are negative reciprocals; here, the product of slopes is -1.
#6
What is the slope of a line parallel to the x-axis?
Undefined
ExplanationLines parallel to the x-axis have an undefined slope, as there is no change in the x-coordinate.
#7
If two lines are parallel, what can be said about their slopes?
Their slopes are equal.
ExplanationParallel lines have equal slopes; their inclinations in the same direction are the same.
#8
What is the slope of a line parallel to the line passing through points (3, 5) and (7, 11)?
2
ExplanationThe slope between the given points is (11-5)/(7-3) = 2; parallel lines share the same slope.
#9
Given the equation 2x + 3y = 9, what is the equation of a line parallel to it passing through the point (-1, 4)?
2x + 3y = 11
ExplanationParallel lines have the same slope; rearrange the equation to maintain the slope and satisfy the new point.
#10
What is the general form of the equation for a line parallel to the y-axis?
x = a
ExplanationLines parallel to the y-axis have a constant x-value; their equation is in the form x = a.
#11
If a line passes through points (-2, 3) and (4, -1), what is the equation of a line parallel to it passing through the point (1, 5)?
y = x + 6
ExplanationParallel lines share the same slope; find the slope from the given points and use it with the new point.
#12
If a line passes through points (2, 5) and (-3, 7), what is the equation of a line parallel to it passing through the point (1, -3)?
y = -2x + 7
ExplanationParallel lines share the same slope; find the slope from the given points and use it with the new point.
#13
What is the slope of a line parallel to a vertical line?
Undefined
ExplanationVertical lines have undefined slopes; parallel lines to them also have undefined slopes.
#14
If a line has a slope of 0, what can be said about a line parallel to it?
The parallel line has a slope of 0.
ExplanationParallel lines share the same slope; if one has a slope of 0, the other parallel line also has a slope of 0.
#15
Which of the following statements about parallel lines is true?
They have the same slope but different y-intercepts.
ExplanationParallel lines share a common slope but can have different y-intercepts.
#16
If the equation of a line is 3x - 2y = 8, what is the equation of a line parallel to it and passing through the point (2, -3)?
3x - 2y = 4
ExplanationParallel lines have the same slope; rearrange the equation to maintain the slope and satisfy the new point.
#17
If the equation of a line is y = -2x + 4, what is the slope of a line parallel to it?
-2
ExplanationParallel lines have the same slope; here, it remains -2.
#18
If the equation of a line is 3x + 2y = 8, what is the equation of a line parallel to it and passing through the point (2, -3)?
3x + 2y = 4
ExplanationParallel lines have the same slope; rearrange the equation to maintain the slope and satisfy the new point.
#19
If the equation of a line is 4x - 2y = 6, what is the equation of a line parallel to it and passing through the point (-3, 5)?
4x - 2y = 4
ExplanationParallel lines have the same slope; rearrange the equation to maintain the slope and satisfy the new point.