Answer:
[tex]y = -x[/tex]
Step-by-step explanation:
Given
[tex]x: 1\ \ ||\ 2\ \ \ ||\ \ \ 3\ ||\ \ 4\ ||\ \ \ 5\ ||\ \ \ 6\ ||\ \ 7\ ||\ \ \ 8\ ||\ 9\ \ \ ||\ \ 10\ ||\ \ \ 11\ ||\ 12\\ y: -1 || -2|| -3 || -4 || -5 || -6|| -7 || -8 || -9 || -10 || -11 || -12[/tex]
Required
Write the equation of the line;
Start by picking any two corresponding x and y values
[tex](x_1,y_1) = (1,-1)[/tex]
[tex](x_2,y_2) = (12,-12)[/tex]
Next, determine the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-12 - (-1)}{12 - 1}[/tex]
[tex]m = \frac{-12 +1}{11}[/tex]
[tex]m = \frac{-11}{11}[/tex]
[tex]m = -1[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - (-1) = -1(x - 1)[/tex]
[tex]y + 1 = -x +1[/tex]
[tex]y = -x[/tex]
Hence, the line equation is:
[tex]y = -x[/tex]
