Question

Write an equation that represents the line.
Use exact numbers.

Answer 1

y = - 2x - 3

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, - 3) and (x₂, y₂ ) = (1, - 5) ← 2 points on the line

m =
`(-5-(-3))/(1-0)` =
`(-5+3)/(1)` =
`(-2)/(1)` = - 2

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - 2x - 3 ← equation of line

Answer 2

y = -2x -3

Explanation:

To write an equation we need two points that the line cuts through.

we then use the formula: Gradient = Rise/Run

the points chosen are (0,-3) and (1,-5)

Gradient = (-5--3)/(1-0)

= -2

to write the equation we need one known point, gradient and one unknown point say (x,y).

we therefore use the formula for gradient/slope

G = Rise/Run

-2 = y+3/x-0

-2x = y + 3

y = -2x -3