Question

What is an
equation of the line that passes through the points (-6,5) and (6, 7)?

Answer 1

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

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. This form is known as the slope-intercept form.

Use the gradient formula below to find the value of m:

`gradient = (y1 - y2)/(x1 - x2)`

*(x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate.

`m = (7 - 5)/(6 - ( - 6)) \\ m = (2)/(12) \\ m = (1)/(6)`

Substitute the value of m into the equation:

y= ⅙x +c

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

When x= 6, y= 7,

`7 = (1)/(6) (6) + c \\ 7 = 1 + c \\ c = 7 - 1 \\ c = 6`

Thus, the equation of the line is y= ⅙x +6.