Question

In the linear equation, k is a constant and k is not equal to 3. When graphed in the xy plane, what is the slope of the line?

A. k
B. -k
C. 1
D. -1

Answer 1

The slope of the line represented by the linear equation, regardless of the value of k, is k. Thus option a is correct.

Explanation:

In a linear equation y = mx + b, where m represents the slope of the line, the coefficient of x is the slope. When the linear equation is written in the form y = kx + b, the coefficient 'k' represents the slope. Therefore, the slope of the line is denoted by 'k' in this equation. Regardless of the value of 'k', it remains the slope of the line.

The slope of a line refers to how steep or flat the line is. It determines the rate at which the line rises or falls concerning the horizontal axis. For a linear equation in the form y = kx + b, 'k' is the slope of the line. If 'k' is positive, the line slopes upward from left to right. If 'k' is negative, the line slopes downward from left to right. Therefore, the value of 'k' directly signifies the slope's magnitude and direction.

In this case, the linear equation mentioned in the question is y = kx + b. As 'k' is the coefficient of x in the equation, the slope of the line represented by this equation is 'k'. This slope remains constant, irrespective of the actual value of 'k' chosen for the equation. Thus, the correct answer is A. k, as it represents the slope of the line in the given linear equation. Thus option a is correct.

Answer 2

The slope of the line in the given linear equation is k.

Therefore the correct option is A.

Explanation:

In a linear equation of the form
`\(y = mx + b\)` , where m is the slope, k in this case represents the slope of the line. Therefore, the correct answer is A. k. The slope of a linear equation indicates the rate at which one variable changes concerning another. In this context, for every unit change in the x-direction, the corresponding change in the y-direction is represented by the value of k.

When k is not equal to 3, it implies that the line is not perfectly vertical or horizontal. If k were 3, the line would be perfectly vertical, and if k were -3, the line would be perfectly horizontal. The conditions set in the question suggest that the line has a non-zero slope, eliminating options C and D.

Understanding the significance of k in the context of slope is crucial. It represents the steepness of the line. A positive k indicates an upward slope, while a negative k indicates a downward slope. Therefore, in the given linear equation, the slope of the line is accurately represented by option A, which is k.

Therefore the correct option is A.