Given:
Table having x and y values
To find:
If the table is a linear one and model the equation if it
For a table to be linear, the change in x values will be constant and the change in y values will also be constant.
change in x:
-5-(-9) = -5 +9 = 4
-1-(-5) = -1 + 5 = 4
change in y:
-7 - (-2) = -7+2 = -5
-17 - (-12) = -17 + 12 = -5
The change in x and change in y have a constant value.
Hence, the relationship is linear
From the option, the equation is written in point-slope form, so we will use the point-slope formula to get our equation
[tex]\begin{gathered} Point\text{ slope:} \\ $y-y_1=m(x-x_1)$ \end{gathered}[/tex]To get the slope, we will pick any two points on the table. Using points (-9, -2) and (-5, -7)
[tex]\begin{gathered} slope\text{ = }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{-7-(-2)}{-5-(-9)} \\ m\text{ = }\frac{-7+2}{-5+9}\text{ = }\frac{-5}{4} \end{gathered}[/tex][tex]\begin{gathered} $y-y_1=m(x-x_1)$ \\ using\text{ point \lparen-9, -2\rparen: }x_1\text{ = -9, y}_1\text{ = -2} \\ \\ y\text{ - \lparen-2\rparen = }\frac{-5}{4}(x\text{ - \lparen-9\rparen\rparen} \\ \\ y\text{ + 2 = }\frac{-5}{4}(x\text{ + 9\rparen} \end{gathered}[/tex][tex]The\text{ relationship is linear; }y\text{ + 2 = }\frac{-5}{4}(x\text{ + 9\rparen \lparen last option\rparen}[/tex]