The variables x=9 and y=15 varies directly. How do you write an equation that relates the variables and find x when y=-5?

Question

Abigail Allen · Accepted Answer

The equation is #y=5/3x#
and
#y=-5color(white)("xx")rarrcolor(white)("xx")x=-3# If #x# and #y# vary directly, then #color(white)("XXX")y=color(blue)c * x# for some constant #color(blue)c# Given that #x=9# and #y=15# is one solution to this equation: #color(white)("XXX")15=color(blue)c * 9# #color(white)("XXX")rarr color(blue)c=15/9=color(blue)(5/3)# So the relating equation is #y=color(blue)(5/3)x# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When #y=-5#, the equation becomes: #color(white)("XXX")-5=color(blue)(5/3)color(green)x# #color(white)("XXX")rarr color(green)x=(-5)xx3/5)=color(green)(-3)#

Genesis Allen · Answer

#x=3# when #y=5# When y increases, x also increases in the same proportion and when y decreases, x also decreases in the same proportion. So #x:y=x1:y1# Or #x/y=(x1)/(y1)# We know, y=15, x=9 and y1=5 #:.x1=((x/y)(y1)=(9/15)5=45/15=3# #x1=3#

Nathan Axel · Answer

undefined To write an equation that relates the variables x and y when they vary directly, you use the formula:

y = kx

where k is the constant of variation.

Given that x = 9 and y = 15 when they vary directly, we can find k:

15 = k * 9
k = 15/9 = 5/3

Now, we can write the equation relating x and y:

y = (5/3)x

To find x when y = -5, we substitute y = -5 into the equation and solve for x:

-5 = (5/3)x
x = -5 * (3/5)
x = -3