What is the equation of the solid boundary line?

and can you explain how you solved it?

solid boundary line: y = -1/2 x + 4

shaded area: y ≥ -1/2 x + 4   and    y < x+1

Step-by-step explanation:

solid boundary line pass (0,4) (2,3)

slope (m) = (3-4) / (2-0) = -1/2

y intercept (b) = 4

equation: y = mx + b        y = -1/2 x + 4

system: y ≥ -1/2 x + 4

dotted line: (0,1) (2,3)

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

b = 1

equation: y = x + 1

system: y < x+1

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

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step-by-step explanation: