Question

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

Answer 1

Answer:

$y = \frac{1}{6} x$

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.

$\boxed{gradient = \frac{y1 - y2}{x1 - x2} }$

Using the above formula,

$m = \frac{1 - ( - 1)}{6 - ( - 6)} \\ m = \frac{1 + 1}{6 + 6} \\ m = \frac{2}{12} \\ m = \frac{1}{6}$

Substitute the value of m into the equation:

$y = \frac{1}{6} x + c$

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

When x=6, y=1,

$1 = \frac{1}{6} (6) + c \\ 1 = 1 + c \\ c = 1 - 1 \\ c = 0$

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