Question

50 POINTS FOR CORRECT AWNSER

Answer 1

y ≤
`(1)/(2)` x + 3

Explanation:

the equation of the 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 ) = (- 6, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

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

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

y =
`(1)/(2)` x + 3 ← is the equation of the line

the solution lies below the line and on the line.

as line is solid use ≤

y ≤
`(1)/(2)` x + 3

Answer 2

`y\leq (1)/(2) x+3`

Explanation:

slope intercept form is
`y=mx+b` where
`m` is the gradient and
`b` is the y-intercept (the number at which it crosses the y axis)

firstly find the equation for this line:

the gradient can be found with the formula
`(y_(2) -y_(1) )/(x_(2) -x_(1) )`

so the gradient is
`(4-3)/(2-0)=(1)/(2) =0.5`

the y intercept is where it crosses the y axis so it is simply 3

our equation for the line is now
`y=(1)/(2) x+3` but the question is asking for an equality where the shaded area is BELOW the line.

so the inequality is
`y\leq (1)/(2) x+3`