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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)

Sagot :

Answer:

Options C. and D. are correct.

Step-by-step explanation:

Let [tex](x_1,y_1)=(0,5),\,(x_2,y_2)=(2,8)[/tex]

Equation of a line is given by [tex]y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)[/tex]

[tex]y-5=(\frac{8-5}{2-0})(x-0)\\\\y-5=\frac{3}{2}x\\\\2y-10=3x\\3x-2y+10=0[/tex]

Put  [tex](x,y)=(5,11)[/tex]

[tex]3(5)-2(11)+10=15-22+10=3\neq 0[/tex]

Put  [tex](x,y)=(5,10)[/tex]

[tex]3(5)-2(10)+10=15-20+10=5\neq 0[/tex]

Put [tex](x,y)=(6,14)[/tex]

[tex]3(6)-2(14)+10=18-28+10=0[/tex]

Put [tex](x,y)=(30,50)[/tex]

[tex]3(30)-2(50)+10=90-100+10=0[/tex]

Put [tex](x,y)=(40,60)[/tex]

[tex]3(40)-2(60)+10=0\\120-120+10=10\neq 0[/tex]

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

Therefore,

points [tex](6,14),\,(30,50)[/tex] lie on the line through [tex](0,5)[/tex] and [tex](2,8)[/tex]

Options C. and D. are correct.