Answer:
The inequality represented by the graph is y > [tex]\frac{1}{3}[/tex] 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
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , 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 = [tex]\frac{-2--3}{3-0}[/tex] = [tex]\frac{-2+3}{3}[/tex] = [tex]\frac{1}{3}[/tex]
∴ m = [tex]\frac{1}{3}[/tex]
→ Substitute it in the form of the equation above
∴ y = [tex]\frac{1}{3}[/tex] 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 = [tex]\frac{1}{3}[/tex] x + -3
∴ y = [tex]\frac{1}{3}[/tex] 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 > [tex]\frac{1}{3}[/tex] x - 3
∴ The inequality represented by the graph is y > [tex]\frac{1}{3}[/tex] x - 3
