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Sagot :
Answer:
the equation: y - 1.6 = 3(x - 2)
Step-by-step explanation:
To find the equation for the linear relationship of the given table, we use the slope-form of linear equation, which is:
[tex]\boxed{y=mx+c}[/tex]
[tex]\begin{array}{c|c}\cline{1-2}x&y\\\cline{1-2}\\2&1.6\\3&4.6\\4&7.6\\5&10.6\\\\\cline{1-2}\end{array}[/tex]
By substituting the x and y with the data, we can come up with 4 equations:
- [tex]1.6=2m+c\ ...\ [1][/tex]
- [tex]4.6=3m+c\ ...\ [2][/tex]
- [tex]7.6=4m+c\ ...\ [3][/tex]
- [tex]10.6=5m+c\ ...\ [4][/tex]
We can pick any 2 of the above equations to find out the value of m and c. Let's say we pick the 1st & 2nd equations:
[tex]\begin{aligned}2m+c&=1.6\\3m+c&=4.6\\-----&---\ (-)\\-m&=-3\\m&=3\end{aligned}[/tex]
Substituting m with 3 for the 1st equation:
[tex]\begin{aligned}2m+c&=1.6\\2(3)+c&=1.6\\c&=1.6-6\\c&=-4.4\end{aligned}[/tex]
Hence, the equation:
[tex]\begin{aligned}y&=3x-4.4\\y-1.6&=3x-6\\\bf y-1.6&\bf =3(x-2)\end{aligned}[/tex]
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