MATH SOLVE

9 months ago

Q:
# which inequality is shown in this graph?

Accepted Solution

A:

Answer:The inequality shown in the graph is y ≤ -3x + 3 ⇒ CStep-by-step explanation:The linear form of the equation of a line is y = m x + b, wherem is the slope of the line and m = Δy/ΔxΔx = x2 - x1 and Δy = y2 - y1b 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