MATH SOLVE

2 months ago

Q:
# 1. For the data table, does y vary directly with x? If it does, write equation for the direct variation. x|y 10|15 16|24 20|30A. Yes; y=1.5xB. Yes; y=2xC. Yes; y=x+5D. No there is no direct variation.2. For the data table, does y vary directly with x? If it does, write equation for the direct variation. x|y 32|24 16|8 8|6A. Yes; y=0.5xB. Yes; y=2xC. Yes; y=1.5xD. No there is no direct variation.Thank you!

Accepted Solution

A:

Answer:Part 1) Option A. Yes; y=1.5xPart 2) Option D. No there is no direct variationStep-by-step explanation:we know thatA relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Part 1) we have the points(10,15),(16,24),(20,30)Find the value of the constant of proportionality k[tex]k=y/x[/tex]For x=10, y=15substitute[tex]k=15/10=1.5[/tex]For x=16, y=24substitute[tex]k=24/16=1.5[/tex]For x=20, y=30substitute[tex]k=30/20=1.5[/tex]The value of the constant k is the same for the three ordered pairsThe linear equation is [tex]y=1.5x[/tex]thereforey vary directly with xPart 2) we have the points(32,24),(16,8),(8,6)Find the value of the constant of proportionality k[tex]k=y/x[/tex]For x=32, y=24substitute[tex]k=24/32=0.75[/tex]For x=16, y=8substitute[tex]k=8/16=0.5[/tex]For x=8, y=6substitute[tex]k=6/8=0.75[/tex]The value of the constant k is not the same for the three ordered pairsthereforey not vary directly with x