Question

Select all the points that are on the line through LaTeX: (0,5)( 0 , 5 ) and LaTeX: (2,8)( 2 , 8 ). Group of answer choices LaTeX: (4,11) ( 4 , 11 ) LaTeX: (5,10) ( 5 , 10 ) LaTeX: (6,14) ( 6 , 14 ) LaTeX: (30,50) ( 30 , 50 ) LaTeX: (40,60)

Answer 1

The points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).

Explanation:

The equation of the line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

So, the equation of the line passing through two points (0,5) and ( 2, 8 ) is

`y-5=(8-5)/(2-0)(x-0)`

`\Rightarrow y=1.5x+5\cdots(i)`

For the point (4,11), pout x=4 in equation (i), we have

`y=1.5*4 +5=11`, which is given y coordinate, hence this point (4,11) lies on the line.

For the point (5,10), pout x=5 in equation (i), we have

`y=1.5*5 +5=12.5,` which is not the given y coordinate, hence the point (5,10) doesn't lie on the line.

For the point (6,14), pout x=6 in equation (i), we have

`y=1.5*6 +5=14`, which is the given y coordinate, hence the point (6,14) lies on the line.

For the point (30,50), pout x=30 in equation (i), we have

`y=1.5*30 +5=50`, which is the given y coordinate, hence the point (30,50) lies on the line.

For the point (40,60), pout x=40 in equation (i), we have

`y=1.5*40 +5=65`, which is not the given y coordinate, hence the point (40,60) doesn't lie on the line.

Hence, the points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).