Answer:
[tex]y = \frac{1}{6} x[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the above formula,
[tex]m = \frac{1 - ( - 1)}{6 - ( - 6)} \\ m = \frac{1 + 1}{6 + 6} \\ m = \frac{2}{12} \\ m = \frac{1}{6} [/tex]
Substitute the value of m into the equation:
[tex]y = \frac{1}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates.
When x=6, y=1,
[tex]1 = \frac{1}{6} (6) + c \\ 1 = 1 + c \\ c = 1 - 1 \\ c = 0[/tex]
Thus, the equation of the line is y=⅙x.
