Answer:
The equation is:
[tex]y = -x + 7[/tex]
Step-by-step explanation:
Given the endpoints of a side of a rectangle
Finding the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:6\right),\:\left(x_2,\:y_2\right)=\left(6,\:1\right)[/tex]
[tex]m=\frac{1-6}{6-1}[/tex]
[tex]m=-1[/tex]
Using the point-slope form of a line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -1 and the point (1, 6)
[tex]y - 6 = -1 (x - 1)[/tex]
[tex]y - 6 = -x + 1[/tex]
[tex]y = -x + 1 + 6[/tex]
[tex]y = -x + 7[/tex]
Thus, the equation is:
[tex]y = -x + 7[/tex]
