#1
What is the equation of a line in slope-intercept form?
y = mx + b
Explanationy = output, m = slope, x = input, b = y-intercept
#2
Which of the following pairs of lines are parallel?
y = x + 4 and y = -x - 4
ExplanationParallel lines have the same slope.
#3
What is the slope of a line parallel to the x-axis?
0
ExplanationLines parallel to the x-axis have a slope of 0.
#4
In a Cartesian coordinate system, where is the origin located?
At (0, 0)
ExplanationThe origin is the point (0, 0) where the x-axis and y-axis intersect.
#5
In a right-angled triangle, if one leg is 3 units long and the other is 4 units long, what is the length of the hypotenuse?
5 units
ExplanationPythagorean theorem: a^2 + b^2 = c^2, where a and b are legs and c is the hypotenuse.
#6
What is the equation of a line parallel to the y-axis?
x = 0
ExplanationLines parallel to the y-axis have an equation of the form x = constant.
#7
What is the midpoint of the line segment with endpoints (2, 5) and (8, 11)?
(6, 8)
ExplanationMidpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2)
#8
Which of the following statements is true about perpendicular lines?
Their slopes are negative reciprocals.
ExplanationPerpendicular lines have slopes that are negative reciprocals of each other.
#9
What is the distance between the points (3, 4) and (7, 1)?
6
ExplanationDistance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2)
#10
Which of the following represents a vertical line?
x = -4
ExplanationVertical lines have the equation of the form x = constant.
#11
Which of the following represents the equation of a horizontal line?
y = -2
ExplanationHorizontal lines have a slope of 0.
#12
What is the formula to calculate the slope of a line passing through two points (x1, y1) and (x2, y2)?
(y2 - y1) / (x2 - x1)
ExplanationSlope formula: (change in y) / (change in x)
#13
If two lines are perpendicular, what is the product of their slopes?
0
ExplanationProduct of slopes of perpendicular lines equals zero.
#14
If two lines are parallel, what can be said about their slopes?
They are equal.
ExplanationParallel lines have equal slopes.
#15
What are the coordinates of the point that divides the line segment with endpoints (-3, 5) and (7, -1) into two equal parts?
(2, 2)
ExplanationMidpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2)
#16
Which of the following statements is true regarding concurrent lines?
They always intersect at the same point.
ExplanationConcurrent lines intersect at a common point.
#17
Which of the following is true about skew lines?
They never intersect.
ExplanationSkew lines do not lie in the same plane and thus never intersect.