Question

Which system is represented in the graph?

Answer 1

y < x - 3

y < x² - 6x - 7

Explanation:

Linear line:

pass through (0, -3) & (7, 4)

`(y-y1)/(y2-y1) =(x-x1)/(x2-x1)`

`(y-(-3))/(4-(-3)) = (x-0)/(7-0)`

7(y+3) = 7x

y + 3 = x

y = x - 3

since the shaded area is below the linear line → y < x - 3

Parabola:

pass through (-1,0) & (7,0) → roots = -1 & 7

y = a(x-(-1))(x-7)

y = a(x+1)(x-7)

pass through (3,16)

-16 = a(3+1)(3-7)

-16 = -16a

a = 1

∴ parabola: y = (x+1)(x-7)

y = x²-6x-7

since the shaded area is below the parabola → y < x² - 6x - 7