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juin [17]
3 years ago
13

Please answer, thank you and have a nice day

Mathematics
1 answer:
taurus [48]3 years ago
8 0

Answer:

The inequality represented by the graph is y >  \frac{1}{3} x - 3

Step-by-step 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 = \frac{y2-y1}{x2-x1} , where

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

<em>To find the inequality represented by the graph, find at first the equation of the line</em>

∵ 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 = \frac{-2--3}{3-0} = \frac{-2+3}{3} = \frac{1}{3}

∴ m =  \frac{1}{3}

→ Substitute it in the form of the equation above

∴ y =  \frac{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 =  \frac{1}{3} x + -3

∴ y =  \frac{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 >  \frac{1}{3} x - 3

∴ The inequality represented by the graph is y >  \frac{1}{3} x - 3

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