Answer:
The inequality represented by the graph is y > [tex]\frac{1}{2}[/tex] x + 2
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 (value y at x = 0)
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
From the given figure
∵ The line passes through points (0, 2) and (2, 3)
∴ x1 = 0 and y1 = 2
∴ x2 = 2 and y2 = 3
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{3-2}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
∴ m = [tex]\frac{1}{2}[/tex]
→ b is the value of y at x = 0
∵ At x = 0, y =2
∴ b = 2
→ Substitute the value of m and b in the form of the equation above
∵ y = [tex]\frac{1}{2}[/tex] x + 2
∴ The equation of the line is y = [tex]\frac{1}{2}[/tex] x + 2
∵ The line is dashed
∵ The shaded area is over the line
∴ The sign of inequality is >
→ Replace = in the equation by >
∴ y > [tex]\frac{1}{2}[/tex] x + 2
∴ The inequality represented by the graph is y > [tex]\frac{1}{2}[/tex] x + 2
