Question

Write an equation that represents the line. (2,-2) and (-2,-6)

Answer 1

y = x - 4

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (- 2, - 6)

m =
`(-6+2)/(-2-2)` =
`(-4)/(-4)` = 1, thus

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, - 2), then

- 2 = 2 + c ⇒ c = - 2 - 2 = - 4

y = x - 4 ← equation of line

Answer 2

Explanation:

Gradient of a line is (x-1-x2)+(y1-y2)

(2--2) +(-2--6)

(4)+(4)

(8)

the gradient of the line is 8