### Chapter 6 - Algebra Coach Exercises

**Algebra Coach Exercise on finding the equation
of a straight line.**

- The graph of a certain straight line contains the two points (2, 3) and (4, 9).
Find the equation of the straight line.

To do this drag-and-drop the following text into the
Algebra Coach’s listbox and click the Substitute button.
The result will be the first of two equations containing *m* and *b*:
x = 2, y = 3, y = m x + b

Clear the Algebra Coach’s listbox and drag-and-drop the following text into it
and click the Substitute button. The result will be the second of two equations containing *m* and *b*:
x = 4, y = 9, y = m x + b

Clear the Algebra Coach’s listbox again and drag *both* equations for *m* and *b*
(one after the other) into it and click on the Solve by elimination button.
When done, the result should be the solution b = −3 and m = 3.
This means that the equation of the straight line is
*y* = 3 *x* − 3.

- The graph of a certain straight line contains the two points (4, 13) and (8, 21).
Find the equation of the straight line.

To do this drag the following text into the
Algebra Coach’s listbox and click the Substitute button.
The result will be an equation containing *m* and *b*:
x = 4, y = 13, y = m x + b

Clear the Algebra Coach’s listbox and drag-and-drop the following text into it
and click the Substitute button. The result will be a second equation containing *m* and *b*:
x = 8, y = 21, y = m x + b

Clear the Algebra Coach’s listbox again and drag *both* equations for *m* and *b*
(one after the other) into it and click on the Solve by elimination button.
When done, the result should be the solution b = 5 and m = 2.
This means that the equation of the straight line is
*y* = 2 *x* + 5.

**Algebra Coach Exercise on graphs of
functions, graphs of relations and parametric plots.**

Graph each of the following functions or relations or construct the parametric plot.
To do this in the Algebra Coach drag-and-drop
each of these problems into the Algebra Coach and click the Graph button.
For question 5, set the option that “the letter p represents the number π”.
- x^2 / 16 + y^2 / 4 = 1
- y = x + 3, y = -2 x + 6
- x^2 - 12 y + y^3 = 30, x^2 - 12 y + y^3 = 10
- x^2 + y^2 = 9, (x-2)^2 + (y-4)^2 = 4
- x = 4 t cos (4 p t), y = 4 t sin (4 p t)

**Algebra Coach Exercise on using graphs to
solve equations.**

Each problem contains an equation to be solved graphically. To do this in the
Algebra Coach drag-and-drop the suggested function
into the Algebra Coach and click the Graph button. The *x* intercepts of the graph
are the solutions of the equation.
- Equation to solve:
*x*/5 = sin(*x*). Suggested function to graph: y = sin(x) - x/5
- Equation to solve:
*x*^{ 2} = *x*^{ 4} − 5. Suggested function to graph: y = x^4 - x^2 - 5
- Equation to solve: sin(
*x*) = 0.6. Suggested function to graph: y = sin(x) - 0.6