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

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

move it to the other side

step-by-step explanation: