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.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Let $(x_1,y_1)=(4,7)$ and $(x_2,y_2)=(4, - 3)$.

Step2: Substitute values into formula

Substitute the values into the slope - formula: $m=\frac{-3 - 7}{4 - 4}=\frac{-10}{0}$. Division by zero is undefined.

Step3: Analyze the line

The two points $(4,7)$ and $(4,-3)$ have the same $x$ - coordinate. A line passing through two points with the same $x$ - coordinate is a vertical line.

Answer:

The line is a vertical line and the slope is undefined.