Question

What should I write for the explanation??plz help

Answer 1

Proof

Explanation:

"The y-intercept is - 2" and now I think the best way to prove the gradient is to prove it mathematically taking coordinates of the line and using:

`m = (y - y)/(x - x)`

So I'll take the coordinates (6,0) and (0,-2) and substitute them in the formula for the gradient.

`m = ( - 2 - 0)/(0 - 6) = ( - 2)/( - 6) = (1)/(3)`

I hope this helps.

Answer 2

y = - 2 +
`(1)/(3)` x

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 ) = (0, - 2) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m =
`(0+2)/(6-0)` =
`(2)/(6)` =
`(1)/(3)`

The line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y =
`(1)/(3)` x - 2 , or

y = - 2 +
`(1)/(3)` x