Question

The standard form of a linear equation is Ax + By = C. If B = 0 and A and Care positive, which best describes the

graph of this equation?
A The graph is a vertical line.
B The graph is a horizontal line.
C The graph is a line with a positive slope.
D The graph is a line with a negative slope.

Answer 1

With B = 0 in the linear equation Ax + By = C, and both A and C positive, the graph is a vertical line that crosses the x-axis at C/A.

Step-by-step explanation:

If B = 0 in the standard form of a linear equation, Ax + By = C, and both A and C are positive, this results in an equation of the form Ax = C. Since B, which is the coefficient of y, equals zero, the equation does not depend on y; therefore no matter what value y takes, x will always be C/A. This describes a vertical line since for all values of y, x remains constant.

To visualize this, if x is a positive number and the line must cross the x-axis at that number (since C and A are positive), there will be no change in x regardless of the value of y. Hence, the graph is a vertical line that crosses the x-axis at the point (C/A, 0).

The correct answer to the student's question is: A. The graph is a vertical line.