Slope intercept form for a line containing 4,2 that is parallel to the line y-2 = 3(x+7)

y-2 = 3(x+7) put it in y=mx+b form (slope intercept)

y-2 = 3(x+7) distribute 3

y-2 = 3x+21  add 2 to both sides

+2         +2

y = 3x + 23

so now the slope of that is 3 so the new equation has a slope of 3 because parallel slopes are equal.  

my new line has a slope of 3 and point (4,2)

so we use point slope formula y-y1 = m(x-x1)

y-2 =3(x-4) put it in y=mx+b form (slope intercept)

y-2 = 3(x-4) distribute 3

y-2 = 3x -12  add 2 to both sides

+2         +2

y = 3x + 10 which is you line slope intercept with parallel slope and contains (4,2)  

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: