Answered

linear relationship is shown in the table. x2345 y1.64.67.610.6 Which equation models the relationship? y 1.6 = –3x 2) y 1.6 = 3(x 2) y – 1.6 = 3(x – 2) y – 1.6 = –3(x – 2)



Answer :

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]

Other Questions