Question

A line passes through the points (2,4) and (5,6) .

Select Yes or No to tell whether each equation describes this line.

Equation Yes No
y−6=32(x+5)
​y−4=23(x−2)​
​y−4=32(x+2)​
​y−6=23(x−5)​

Answer 1

Option B and D are correct.

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
`(x_1,y_1)` and
`(x_2, y_2)`

then the general form
`y -y_1=m(x-x_1)` for linear equations where m is the slope given by:

`m =(y_2-y_1)/(x_2-x_1)`

First calculate slope for the points (2, 4) and (5, 6);

`m = (y_2-y_1)/(x_2-x_1) =(6-4)/(5-2) = (2)/(3)`

then, by point slope intercept form;

`y-4=(2)/(3)(x-2)`

* 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 = (y_2-y_1)/(x_2-x_1) =(4-6)/(2-5) = (-2)/(-3)= (2)/(3)`

then, by point slope intercept form;

`y-6=(2)/(3)(x-5)`

Yes, the only equation of line from the given options which describes the given line are;

`y-4=(2)/(3)(x-2)` and
`y-6=(2)/(3)(x-5)`