How do you find the range given x=3-2t and y=2+3t for -2 ≤ t ≤ 3?

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Answer 1 · 2018-04-23T18:19:18

#[-2,8]#

the range is the difference between the least point and highest point from the #x# axis

which are the #y# values

#y=2+3t#

Substiutute

#t=-2# #rarr" "##y=-2#

#t=3# #rarr" "##y=8#

so your range will be #[-2,8]#

Answer 2 · 2018-04-23T18:27:57

Given: #y=2+3t" [1]"# and #-2 <= t <= 3" [2]"#

Solve equation [1] for #t# in terms of #y#:

#y=2+3t" [1]"#

#3t = y-2#

#t = (y-2)/3" [1.1]"#

Substitute equation [1.1] into inequality [2]:

#-2 <= (y-2)/3 <= 3#

Multiply the inequality by 3:

#-6 <= y-2 <= 9#

Add 2 to the inequality:

#-4 <= y <= 11 larr# this is the range.