If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?

Question

Eva Adamson · Accepted Answer

#y=-8# If #y# varies directly with #x#, an equation to express this can be: #y=mx# #1#. Since #y=4# when #x=12#, substitute the values into #y=mx# to determine the value of #m#. #y=mx# #4=m(12)# #color(blue)(m=1/3)# #2#. With the value of #color(blue)m# known, substitute #color(blue)m# and #x=-24# into #y=mx# to determine the value of #y#. #y=color(blue)(1/3)x# #y=color(blue)(1/3)(-24)# #y=1/color(red)cancelcolor(black)(3)^1(-color(red)cancelcolor(black)(24)^8)# #color(green)(y=-8)# #:.#, #y=-8# when #x=-24#.

Eli Assouline · Answer

undefined To find $ y $ when $ x = -24 $, use the direct variation equation $ y = kx $, where $ k $ is the constant of variation. First, find the value of $ k $ using the given dataTo find $ y $ when $ x = -24 $, use the direct variation equation $ y = kx $, where $ k $ is the constant of variation. First, find the value of $ k $ using the given  $ y = 4 $ when $ x = 12 $. $ k = \frac{y}{x} = \frac{4}{12} = \frac{1}{3} $. Then, use this value of $ k $ to find $ y $ when $ x = -24 $. $ y = \frac{1}{3} \times (-24) = -8 $. Therefore, when $ x = -24 $, $ y = -8 $.