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41 votes
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)

User Max Worg
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1 Answer

27 votes
27 votes

Answer:

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.

User Cbjeukendrup
by
2.4k points