ANSWER
[tex]\begin{gathered} y-6=-\frac{5}{4}(x+2) \\ \\ y-1=-\frac{5}{4}(x-2) \\ \\ y-3.5=-1.25x \end{gathered}[/tex]
EXPLANATION
We want to find the equation that represents the data in the given table.
The table represents a linear relationship between x and y. This implies that the equation representing the table (in point-slope) form can be written generally as:
[tex]y-y_1=m(x-x_1)[/tex]
where m = slope
(x1, y1) = a pair of points from the table
First, we have to find the slope, m, by using two pairs of points from the table and applying the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us use the points (-2, 6) and (2, 1):
[tex]\begin{gathered} m=\frac{1-6}{2-(-2)}=\frac{1-6}{2+2} \\ \\ m=\frac{-5}{4} \\ \\ m=-\frac{5}{4} \end{gathered}[/tex]
Now, substitute the values for m and (x1, y1) into the point-slope formula:
[tex]\begin{gathered} y-6=-\frac{5}{4}(x-(-2)) \\ \\ y-6=-\frac{5}{4}(x+2) \end{gathered}[/tex]
We can also use another pair of points on the table for (x1, y1). Let us use (2, 1):
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
Also, we can simplify either equation as follows:
[tex]\begin{gathered} y-6=-\frac{5}{4}x-\frac{5}{2} \\ \\ y-6=-1.25x-2.5 \\ \\ y-6+2.5=-1.25x \\ \\ y-3.5=-1.25x \end{gathered}[/tex]
Therefore, the correct options are:
[tex]\begin{gathered} y-6=-\frac{5}{4}(x+2) \\ \\ y-1=-\frac{5}{4}(x-2) \\ \\ y-3.5=-1.25x \end{gathered}[/tex]
