1.
Ax +by +c=0.
Which of the following defines the above equation?
Correct Answer
A. Linear equation
Explanation
The given equation, ax + by + c = 0, represents a linear equation. A linear equation is an equation in which the variables (x and y in this case) are raised to the first power and are not multiplied or divided by each other. The equation is in the form of a straight line when graphed, hence the name "linear equation". Therefore, the correct answer is "Linear equation".
2.
Y=mx+b, What does m represent?
Correct Answer
B. Slope
Explanation
The variable "m" in the equation y=mx+b represents the slope. The slope is a measure of how steep a line is and determines the rate of change between the y and x variables. In this equation, "m" is multiplied by the x variable, indicating that it determines the change in y for a given change in x. Therefore, the correct answer is "Slope".
3.
Which of the following is a linear equation?
Correct Answer
D. All of the above
Explanation
All of the given equations are linear equations. A linear equation is an equation in which the highest power of the variable is 1. In the first equation, 5x = 6 + 3y, both x and y have a power of 1. In the second equation, y = 2x + 1, both x and y have a power of 1. In the third equation, y/2 = 3 - x, both y and x have a power of 1. Therefore, all of the given equations are linear equations.
4.
Find y in the following equation.
y/2 = 3
Correct Answer
A. 6
Explanation
To find y in the equation y/2 = 3, we need to isolate y. To do this, we can multiply both sides of the equation by 2. This cancels out the division by 2 on the left side, leaving us with y = 6. Therefore, the value of y is 6.
5.
Which of the following is a linear equation?
Correct Answer
B. y/2 = 3
Explanation
A linear equation is an equation that can be written in the form y = mx + b, where m and b are constants. In the given options, only the equation y/2 = 3 can be written in this form. Therefore, y/2 = 3 is the only linear equation among the options provided.
6.
Which of the following is not a linear equation?
Correct Answer
D. None of the above
Explanation
All of the given equations are linear equations. The first equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. The second equation is also in the form of y = mx + b, with a slope of 3 and a y-intercept of -6. The third equation is in the form of ax + b = 0, which can be rearranged to the form of y = mx + b by dividing both sides by 5. Therefore, all of the given equations are linear equations, so the correct answer is "None of the above".
7.
Which of the following is not a linear equation?
Correct Answer
A. Y2 − 2 = 0
Explanation
The equation y2 − 2 = 0 is not a linear equation because it contains a squared term (y2), which makes it a quadratic equation. Linear equations have variables raised to the power of 1 (y, x) and do not include squared terms.
8.
Which of the following is defined as the equation for a straight line?
Correct Answer
A. Linear Equation
Explanation
A linear equation is defined as the equation for a straight line. It is a mathematical equation that represents a straight line on a graph. The equation is in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. This equation is used to describe relationships between variables that show a constant rate of change.
9.
Which of the following is a linear equation?
Correct Answer
A. Ax + By + C = 0
Explanation
The equation Ax + By + C = 0 is a linear equation because it represents a straight line when graphed. The variables x and y have a power of 1, and there are no other terms or operations that would make the equation non-linear.
10.
Find y in 3x+5=7
Correct Answer
D. None of the above