Answer:
A. The slope is [tex]\frac{3}{2}[/tex]
B. the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point.
Step-by-step explanation:
PART A: Slope
Given tangent line;
[tex]y = \frac{3x}{2} + \frac{9}{2}[/tex]
The slope of the tangent line is equal to the derivative of the function;
[tex]\frac{dy}{dx} =\frac{3}{2}[/tex]
the slope = [tex]\frac{3}{2}[/tex]
PART B: Correct statement that describe the slope of a tangent line:
A secant line is a straight line joining two points on a function and the slope of the function is equal to average rate of change of the function between the two points.
A tangent line is a straight line that touches a function at only one point, and the slope of the function is equal to the instantaneous rate of change of the function at that one point.
Thus, the correct statement is " the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point".
