Respuesta :
ANSWER
[tex]\begin{gathered} y=x-12 \\ y=-6,x=6 \\ x=-10,y=-22 \end{gathered}[/tex]EXPLANATION
The first step is to find the equation that represents the function given.
The function is a linear function. The general form of a linear function is given as:
[tex]y=mx+b_{}[/tex]where m = slope; b = y intercept
To find the slope, we can apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x₁, y₁) and (x₂, y₂) are two sets of data points from the table
Let us pick (32, 20) and (14, 2) as (x₁, y₁) and (x₂, y₂).
Therefore:
[tex]\begin{gathered} m=\frac{2-20}{14-32} \\ m=\frac{-18}{-18} \\ m=1 \end{gathered}[/tex]Now, find the function by using the point-slope method:
[tex]y-y_1=m(x-x_1)[/tex]Therefore:
[tex]\begin{gathered} y-20=1(x-32) \\ y-20=x-32 \\ y=x-32+20 \\ y=x-12 \end{gathered}[/tex]That is the rule/function that represents the table.
To find the value of x when y is -6, substitute y with -6 in the function above and solve for x:
[tex]\begin{gathered} -6=x-12 \\ \Rightarrow x=-6+12 \\ x=6 \end{gathered}[/tex]To find the value of y when x is -10, substitute x with -10 in the function and solve for y:
[tex]\begin{gathered} y=-10-12 \\ y=-22 \end{gathered}[/tex]
