The assignments below are meant to practice the following:

a. calculating the equation of a line through a given point and with a given slope;

b. calculating the equation of a line through two given points;

c. calculating the tangent line at a point of a graph of a function.

1. Calculate the slope of the tangent line at the point of the graph of the function:

2. Calculate the slope of the tangent line at the point of the graph of the function:

3. Calculate the slope of the tangent line at the point of the graph of the function:

4. Calculate the equation of the line through the point with slope .

5. Calculate the equation of the line through the point parallel to the line:

6. Calculate the equation of the tangent line at the point of the graph of the function:

7. Calculate the equation of the tangent line(s) of the graph of the function:

parallel to the tangent line at the point of the graph of the function:

8. The line:

intersects the parabola:

in two points A en B.

The tangent lines at these points intersect in a point C.

Calculate the coordinates of C.

9. The graph of the function:

intersects the -axis in point A.

The tangent line at this point of the graph intersects the -axis. Calculate the coordinates of this intersection point.

10. Give the equation of the line through the points:

and