Question

What is an equation of the line that passes through the points (6, -7) and (-6, 3))? Put your answer in fully reduced form.

Answer 1

The equation of the line is y =
`-(5)/(6)` x - 2

Explanation:

The form of the linear function is y = m x + b, where

• m is the slope

• b is the y-intercept

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (6, -7) and (-6, 3)

∴ x1 = 6 and y1 = -7

∴ x2 = -6 and y2 = 3

→ Substitute them in the rule of the slope above to find it

∵ m =
`(3--7)/(-6-6)` =
`(3+7)/(-12)` =
`(10)/(-12)` =
`(5)/(-6)`

∴ m =
`-(5)/(6)`

→ Substitute it in the form of the equation above

∴ y =
`-(5)/(6)` x + b

→ Substitute x and y in the equation by x1 and y1

∵ x1 = 6 and y1 = -7

∴ -7 =
`-(5)/(6)` (6) + b

∴ -7 = -5 + b

→ Add 5 to both sides

∵ -7 + 5 = -5 + 5 + b

∴ -2 = b

→ Substitute the value of b in the equation

∴ y =
`-(5)/(6)` x + -2

∴ y =
`-(5)/(6)` x - 2

∴ The equation of the line is y =
`-(5)/(6)` x - 2