Question

Select all the points that are on the line through (0 5) and (2 8) A.(5 11) B.(5 10) C.(6 14) D.(30 50) E.(40 60)

Answer 1

Options C. and D. are correct.

Explanation:

Let
`(x_1,y_1)=(0,5),\,(x_2,y_2)=(2,8)`

Equation of a line is given by
`y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)`

`y-5=((8-5)/(2-0))(x-0)\\\\y-5=(3)/(2)x\\\\2y-10=3x\\3x-2y+10=0`

Put
`(x,y)=(5,11)`

`3(5)-2(11)+10=15-22+10=3\\eq 0`

Put
`(x,y)=(5,10)`

`3(5)-2(10)+10=15-20+10=5\\eq 0`

Put
`(x,y)=(6,14)`

`3(6)-2(14)+10=18-28+10=0`

Put
`(x,y)=(30,50)`

`3(30)-2(50)+10=90-100+10=0`

Put
`(x,y)=(40,60)`

`3(40)-2(60)+10=0\\120-120+10=10\\eq 0`

So, points
`(6,14),\,(30,50)` satisfy the equation
`3x-2y+10=0`

Therefore,

points
`(6,14),\,(30,50)` lie on the line through
`(0,5)` and
`(2,8)`

Options C. and D. are correct.