Because the equation has an [tex]\boxed{\text{exponent of 2}}[/tex], it [tex]\boxed{\text{cannot}}[/tex] 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 [tex]\boxed{\text{varies}}[/tex] so the graph of the equation is a [tex]\boxed{\text{curve}}[/tex]
Therefore, the equation represents a [tex]\boxed{\text{nonlinear}}[/tex] 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.
