Answer:
The inequality shown in the graph is y ≤ -3x + 3 ⇒ C
Step-by-step explanation:
The linear form of the equation of a line is y = m x + b, where
- m is the slope of the line and m = Δy/Δx
- Δx = x2 - x1 and Δy = y2 - y1
- b is the y-intercept (value y at x = 0)
From the given graph
∵ The line passes through points (0, 3) and (2, -3)
∴ x1 = 0 and x2 = 2
∴ y1 = 3 and y2 = -3
∵ The slope of the line is m = Δy/Δx
∵ Δx = 2 - 0 = 2
∵ Δy = -3 - 3 = -6
∴ m = [tex]\frac{-6}{2}[/tex]
∴ m = -3
∵ b is value y at x = 0
∴ b = 3
→ Substitute m and b in the form of the equation above
∴ y = -3x + 3
∵ The line is solid and the shading area is under the line
∴ The sign of inequality is ≤ ⇒ (smaller than or equal)
→ Change = in the equation by ≤ to get the inequality
∴ y ≤ -3x + 3
∴ The inequality shown in the graph is y ≤ -3x + 3
