Dwayne wrote a two-digit number. he multiplied it by 3, added 18, and divided by 8. his final answer was 9. what number did duwayne write?
given x varies inversely with y, the the equation relating them is
x = ← k is the constant of variation
to find k use the condition x = 6 when y = 10, hence
k = xy = 6 × 10 = 60
x = ← equation of variation
when x = 8, then
8 × y = 60 ( divide both sides by 8 )
y = = 7.5 → b
recall the angle sum identities:
then the left hand side of the equation reduces significantly to give
in general, this occurs for and where is any integer. we get solutions in the interval for , for which we get
is point slope form of equation of a line.
given points are :
(-6,4) and (2,-9) where
we have to find slope by using above points.
m= 9-4 / -)
now, take point and put the value of slope in point-slope form of equation:
y-4=5/4(x+6) is point-slope form of equation for the line that passes through the points (-6,4) and (-2,9) .