Answered

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The table represents some points on the graph of a linear function. Which equation represents the same relationship?A: y-3=-2(x+6)B: y-6 = - 1/2 (x+3)C: y+3=-1/2(x-6)D:y-6=-2(x+3)

The Table Represents Some Points On The Graph Of A Linear Function Which Equation Represents The Same RelationshipA Y32x6B Y6 12 X3C Y312x6Dy62x3 class=

Sagot :

To determine which of the options best defines the table, we will have to determine the equation of the line that defines the table.

To find the equation of a line

let us select the first two points of the table

[tex]\begin{gathered} \text{when } \\ x=-4,\text{ y=2} \\ \text{when} \\ x=-2,\text{ y=1} \end{gathered}[/tex]

We can now use the equation of the line formula

[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-2}{x-(-4)}=\frac{1-2}{-2-(-4)} \\ \\ \frac{y-2}{x+4}=\frac{1-2}{-2+4} \\ \\ \frac{y-2}{x+4}=\frac{-1}{2} \end{gathered}[/tex]

The next step will be

to cross multiply

[tex]y-2=-\frac{1}{2}(x+4)[/tex]

To find the option that conforms to the expression

[tex]\begin{gathered} \text{let us add 5 to both sides} \\ y-2+5=-\frac{1}{2}(x+4)+5 \\ \\ y+3=-\frac{1}{2}x-2+5 \\ y+3=-\frac{1}{2}x+3 \\ \text{This is equivalent to} \\ y+3=-\frac{1}{2}(x-6) \end{gathered}[/tex]

ThusThe correct answer is option C

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