Question

Can you let me know the answer please

Answer 1

y ≤
`(1)/(3)` x - 4

Explanation:

the first step is to obtain the equation of the line.

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

m =
`(-3-(-4))/(3-0)` =
`(-3+4)/(3)` =
`(1)/(3)`

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y =
`(1)/(3)` x - 4 ← equation of the line

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the shaded region below the line indicates the values that are less than y

the solid line indicates that y can equal the values on the line (≤ )

the solution is then

y ≤
`(1)/(3)` x - 4