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Sagot :
We get the two points (9,2) and (12,3) from the table.
Consider the equation
[tex]y=mx+b[/tex]Substitute x=9 and y=2, we get
[tex]2=m(9)+b[/tex][tex]b=2-9m[/tex]Substitute x=12 and y=3 in the equation, we get
[tex]3=m(12)+b[/tex]Substitute b=2-9m to find the value of m.
[tex]3=12m+2-9m[/tex][tex]3-2=3m[/tex][tex]m=\frac{1}{3}[/tex]Substitute m=1/3 in b=2-9m to find the value of b.
[tex]b=2-9(\frac{1}{3})[/tex][tex]b=-1[/tex]Substitute m=1/3 and b=-1 in the equation, we get
[tex]y=\frac{1}{3}x-1[/tex]Verification:
consider the third point (33,10).
Substitute x=33 and b=10 in the equation, we get
[tex]10=\frac{1}{3}\times33-1[/tex][tex]10=11-1[/tex][tex]10=10[/tex]It is verified.
Hence the required equation is
[tex]y=\frac{1}{3}x-1[/tex]
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