Follow the steps below to answer the following question: For what values a and b is the line 2x + y = b tangent to the curve y = ax² at the point with x = -2? (A) Use the limit process, as we did in class, to find the slope of the tangent line to y = ax? when x = -2. (Your answer will contain an a.) The slope of the tangent line to y = ax? whenx = -2 is (B) What is the slope of the line 2x + y = b? The slope of this line is (C) In order for the line 2x + y = b to be tangent to the curve y = ax? at x = -2, we need for the slope of the tangent line to y = ax? at x = -2 to be the same as the slope of the line 2x + y = b. Thus in comparing (A) and (B), we find that a = (D) Lastly, in order for the line 2x + y = b to be tangent to the curve y = ax² at x = -2, the graphs of 2x + y = b and y = ax? must have the same y- coordinate at x = -2. Comparing the y-coordinates of the two graphs tells us that b =

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: