Question

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Answer 1

The inequality represented by the graph is y >
`(1)/(3)` x - 3

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

To find the inequality represented by the graph, find at first the equation of the line

∵ The line passes through points (0, -3) and (3, -2)

∴ x1 = 0 and y1 = -3

∴ x2 = 3 and y2 = -2

→ Substitute them in the rule of the slope above to find it

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

∴ m =
`(1)/(3)`

→ Substitute it in the form of the equation above

∴ y =
`(1)/(3)` x + b

∵ b is the y-intercept ⇒ value y at x = 0

∵ y = -3 at x = 0

∴ b = -3

→ Substitute it in the equation

∴ y =
`(1)/(3)` x + -3

∴ y =
`(1)/(3)` x - 3

→ Let us change it to inequality

∵ The line is dashed

∵ The shading area is above the line

∴ The sign of inequality should be >

∴ y >
`(1)/(3)` x - 3

∴ The inequality represented by the graph is y >
`(1)/(3)` x - 3