Question

marcus plots the point (4, 7) in quadrant i on the coordinate plane. nicole then plots the point (4, -3) in quadrant iv of the same graph. explain what the line that goes through those two points would look like, and evaluate the slope.
the line is a vertical line and the slope is undefined.
sample response: since both points have the same x - coordinate, the line would be vertical. a vertical line has no slope because the run of the graph, which is the denominator, is zero and therefore an undefined fraction.
which of the following did you include in your response?
□ the points have the same x - coordinates.
□ the line would be vertical.
□ the line has no slope.
□ the run = 0, which would create an undefined fraction.

Explanation:

Given points (4, 7) and (4, - 3), their x - values are equal. In coordinate geometry, when x - coordinates of two points are the same, the line connecting them is vertical. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, and for vertical lines, $x_2 - x_1=0$ (run = 0), making the slope undefined.

Answer:

• The points have the same x - coordinates.
• The line would be vertical.
• The line has no slope.
• The run = 0, which would create an undefined fraction.