Answer:
Option B and D are correct.
Step-by-step explanation:
Given: A line passes through the points (2,4) and (5,6).
* Case 1:
If a line passes through the points (2, 4) and (5, 6)
Point slope intercept form:
for any two points
and ![(x_2, y_2)](https://tex.z-dn.net/?f=%28x_2%2C%20y_2%29)
then the general form
for linear equations where m is the slope given by:
![m =\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%20m%20%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
First calculate slope for the points (2, 4) and (5, 6);
![m = \frac{y_2-y_1}{x_2-x_1} =\frac{6-4}{5-2} = \frac{2}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%3D%5Cfrac%7B6-4%7D%7B5-2%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
then, by point slope intercept form;
* Case 2:
If a line passes through the points (5, 6) and (2, 4)
First calculate slope for the points (5, 6) and (2, 4);
![m = \frac{y_2-y_1}{x_2-x_1} =\frac{4-6}{2-5} = \frac{-2}{-3}= \frac{2}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%3D%5Cfrac%7B4-6%7D%7B2-5%7D%20%3D%20%5Cfrac%7B-2%7D%7B-3%7D%3D%20%5Cfrac%7B2%7D%7B3%7D)
then, by point slope intercept form;
Yes, the only equation of line from the given options which describes the given line are;
and