Graphing Equations in Rectangular Coordinates

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Question:

Explain how to graph an equation in the rectangular coordinate system. Question content area bottom Part 1 Choose the correct answer below. A. ​First, find several ordered pairs that are solutions of the equation.​ Next, plot these ordered pairs as points in the rectangular coordinate system.​ Finally, connect the points with a series of line segments. B. ​First, find several ordered pairs that are solutions of the equation.​ Next, plot these ordered pairs as points in the rectangular coordinate system.​ Finally, connect the points with a smooth curve or line. C. ​First, find several ordered pairs that are solutions of the equation.​ Next, draw horizontal lines at all​ y-values in these ordered​ pairs, and draw vertical lines at all​ x-values in these ordered pairs.​ Finally, connect the intersections of the horizontal and vertical lines with a smooth curve or line. D. ​First, find several ordered pairs that are solutions of the equation.​ Next, draw horizontal lines at all​ y-values in these ordered​ pairs, and draw vertical lines at all​ x-values in these ordered pairs.​ Finally, connect the points with a series of line segments. Choose the correct answer below.

Answer:

The correct answer is:

B. ​First, find several ordered pairs that are solutions of the equation. Next, plot these ordered pairs as points in the rectangular coordinate system. Finally, connect the points with a smooth curve or line.

This method is appropriate because it allows for the representation of both linear and non-linear equations accurately. Connecting the points with a smooth curve or line is essential for visualizing the relationship described by the equation, especially for functions that are continuous.