Which system of equations does this graph represent?

The system of equations is y = x - 4 and y = x² - 6

Step-by-step explanation:

The graph has a linear equation represented by a line and a quadratic equation represented by a parabola

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

The form of the quadratic equation is y = a(x - h)² + k, where (h, k) are the coordinates of its vertex point and a is the coefficient of x²

let us use the graph to find each equation

→ Equation the line

∵ The line passes through points (-1, -5) and (2, -2)

∵ m =

∴ m =

∴ m = 1

∵ The line intersected the y-axis at point (0, -4)

∵ b is the value of y at x = 0

∴ b = -4

→ Substitute the values of m and b in the form of the equation above

∴ y = (1)x + (-4)

∴ y = x - 4

→ Equation the parabola

∵ The vertex of the parabola is (0, -6)

∴ h = 0 and k = -6

→ Substitute them in the equation

∴ y = a(x - 0)² + -6

∴ y = ax² - 6

→ To find a choose any point on the parabola and substitute x and y

   by its coordinated

∵ The point (2, -2) lies on the parabola

∴ x = 2 and y = -2

∵ -2 = a(2)² - 6

∴ -2 = 4a - 6

→ Add 6 to both sides

∵ -2 + 6 = 4a - 6 + 6

∴ 4 = 4a

→ Divide both sides by 4

∴ 1 = a

∴ y = (1)x² - 6

∴ y = x² - 6

The system of equations is y = x - 4 and y = x² - 6

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