SOLUTION: here's a table. x y 4 14 8 15.5 12 17 16 18.5 i know the rate of change is 1.5, but how would i find the value of y when x=120?? how about

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: here's a table. x y 4 14 8 15.5 12 17 16 18.5 i know the rate of change is 1.5, but how would i find the value of y when x=120?? how about      Log On

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Question 59322This question is from textbook
: here's a table.
x y
4 14
8 15.5
12 17
16 18.5
i know the rate of change is 1.5, but how would i find the value of y when x=120?? how about finding the value of x when y=50?? This question is from textbook

Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
here's a table.
x y
4 14
8 15.5
12 17
16 18.5
How would i find the value of y when x=120?? how about finding the value of x when y=50??
Your rate of change is the slope between various points. I checked this out and this is indeed a linear relation.
The formula to find the slope between two points is:
highlight%28m=%28y2-y1%29%2F%28x2-x1%29%29
You can choose any two points to find the slope, so let's choose the ones without decimals to make it a little easier.
(x1,y1)=(4,14) and (x2,y2)=(12,17)
m=%2817-14%29%2F%2812-4%29
m=3%2F8
We can now find the equation of the line using the point-slope formula:highlight%28y-y1=m%28x-x1%29%29, m=slope,(x1,y1)=any point on the line.
(x1,y1)=(4,14) and m=3/8
y-14=%283%2F8%29%28x-4%29
8%28y-14%29=8%283%2F8%29%28x-4%29
8y-112=3%28x-4%29
8y-112=3x-12
-3x%2B8y-112=-3x%2B3x-12
-3x%2B8y-112%2B112=112-12
-3x%2B8y=100
-%28-3x%2B8y%29=-100
3x-8y=-100
:
When x=120
3(120)-8y=-100
360-8y=-100
-360+360-8y=-360-100
-8y=-460
-8y/-8=-460/-8
y=115/2
highlight%28y=57.5%29
:
When y=50
3x-8(50)=-100
3x-400=-100
3x-400+400=400-100
3x=300
3x/3=300/3
highlight%28x=100%29
:
If I just blew your mind and you've never seen any of this before, another way you can do this is to plot the points on a graph and using graph paper and a ruler you can approximate the same thing.
:
Happy Calculating!!!