Question

Does the equation y=9x^2+19 represent a linear function?

Answer 1

exponent of 2, cannot, varies, curve, nonlinear.

Answer 2

Because the equation has an $\boxed{\text{exponent of 2}}$, it $\boxed{\text{cannot}}$ be written in the form y = mx+b

When the equation is graphed, the rate of change between different pairs of coordinates on the graph $\boxed{\text{varies}}$ so the graph of the equation is a $\boxed{\text{curve}}$

Therefore, the equation represents a $\boxed{\text{nonlinear}}$ function.

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So in short, y = 9x^2+19 is not linear because it graphs out a curve that isn't a straight line.

More info: The equation y = 9x^2+19 is a quadratic function as the exponent of 2 is the largest exponent. The degree is 2 for the same reason. A parabola will be graphed in this case, which is a curved bowl-like shape. The lowest point of this parabola is at (0,19) which is also the y intercept. There are no x intercepts as this parabola is entirely above the x axis and it goes on forever upward. See the diagram below for the graph of y = 9x^2+19.