#1
Which of the following is the slope-intercept form of a linear equation?
y = mx + b
Explanationy = mx + b represents a linear equation where 'm' is the slope and 'b' is the y-intercept.
#2
What is the slope of a horizontal line?
Zero
ExplanationHorizontal lines have a slope of zero.
#3
In the equation y = mx + b, what does 'b' represent?
Y-intercept
Explanation'b' represents the y-intercept of the line.
#4
In the standard form of a linear equation ax + by = c, what is the constraint on 'a' and 'b'?
a and b cannot be both zero
Explanation'a' and 'b' cannot both be zero in the standard form of a linear equation.
#5
What is the slope of a vertical line?
Undefined
ExplanationThe slope of a vertical line is undefined.
#6
Which of the following is the point-slope form of a linear equation?
y - y₁ = m(x - x₁)
ExplanationThe point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and 'm' is the slope.
#7
If two lines are parallel, what can be said about their slopes?
They have the same slope
ExplanationParallel lines have equal slopes.
#8
What is the determinant of the coefficient matrix for the system of equations 3x - 2y = 7 and 2x + 4y = 5?
10
ExplanationThe determinant of the coefficient matrix is 10.
#9
What is the relationship between the slopes of perpendicular lines?
One slope is negative reciprocal of the other
ExplanationThe slopes of perpendicular lines are negative reciprocals of each other.
#10
What is the solution to the inequality 2x - 3 < 5?
x > 2
ExplanationThe solution to the inequality is x > 2.
#11
What is the solution to the system of equations 2x - y = 3 and x + y = 5?
x = 1, y = 4
ExplanationThe solution to the system is x = 1 and y = 4.
#12
Which of the following statements is true about the system of linear equations with no solution?
The lines are parallel
ExplanationThe lines in the system are parallel and do not intersect.
#13
If a line has an undefined slope, what can be said about its orientation?
It is vertical
ExplanationA line with an undefined slope is vertical.
#14
What is the solution to the system of inequalities:
2x + y ≤ 8 and x - 3y > 4?
x ≤ 3, y ≥ 2
ExplanationThe solution is x ≤ 3 and y ≥ 2.
#15
Which of the following is a consistent and dependent system of linear equations?
x + y = 5, 2x + 2y = 10
ExplanationThe second equation is a multiple of the first, indicating dependency.