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)
Accepted Solution
A:
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.