Respuesta :
The line that represents the relationship between "y" and "x" passes through the origin and the points (k,7) and (-81,-9)
Assuming that "y" varies directly with "x", we can express their relationship as:
[tex]y=mx[/tex]Where "m" represents the slope of the line, also known as coefficient of proportionality or variation.
Using this expression and the known paired values (-81,-9) we can calculate the value of the slope as:
[tex]\begin{gathered} -9=m(-81) \\ m=-\frac{9}{-81} \\ m=\frac{1}{9} \end{gathered}[/tex]The slope of the line is m=1/9 → this value is constant, regardless the values of x and y. Using it you can determine the value of k as follows:
[tex]\begin{gathered} y=\frac{1}{9}x \\ \text{For (k,7)} \\ 7=\frac{1}{9}k \\ k=\frac{7}{\frac{1}{9}} \\ k=7\cdot9 \\ k=63 \end{gathered}[/tex]The value of k is 63
