Question

point x has coordinates (-2, -3) as show in the coordinate plane below. if a line contains both point x and the origin, which of the following points would the line also contain? select all of the points that would lie on the same line as x and the origin. (4, -6) (4, 6) (-4, 6)

Explanation:

Step1: Find the slope of the line through Point X(-2,-3) and the origin (0,0).

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-2,-3)$, so $m=\frac{-3 - 0}{-2 - 0}=\frac{3}{2}$.

Step2: Check the slope for each given point with the origin.

For point $(4,6)$: Using the slope formula with $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(4,6)$, $m=\frac{6 - 0}{4 - 0}=\frac{6}{4}=\frac{3}{2}$.
For point $(4, - 6)$: Using the slope formula with $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(4,-6)$, $m=\frac{-6 - 0}{4 - 0}=-\frac{3}{2}$.
For point $(-4,6)$: Using the slope formula with $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-4,6)$, $m=\frac{6 - 0}{-4 - 0}=-\frac{3}{2}$.

Answer:

B. $(4,6)$