Question

What is an equation of the line that passes through the points (6, 1) and (-6, -1)?

Answer 1

`y = (1)/(6) x`

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.

`\boxed{gradient = (y1 - y2)/(x1 - x2) }`

Using the above formula,

`m = (1 - ( - 1))/(6 - ( - 6)) \\ m = (1 + 1)/(6 + 6) \\ m = (2)/(12) \\ m = (1)/(6)`

Substitute the value of m into the equation:

`y = (1)/(6) x + c`

To find the value of c, substitute a pair of coordinates.

When x=6, y=1,

`1 = (1)/(6) (6) + c \\ 1 = 1 + c \\ c = 1 - 1 \\ c = 0`

Thus, the equation of the line is y=⅙x.