  # BASIC ALGEBRA TOPICS 3-4 REVIEW FOR EXAM

The exam covers concepts learned in Lessons 3.1, 4.1, and 4.2. The following objectives were introduced:

1. Identify the x-axis, y-axis, quadrants, and the origin of an xy plane
2. Identify the x- coordinate and the y -coordinate of an ordered pair .
3. Plot ordered pairs on the xy-plane.
4. Identify the signs of the coordinates in each quadrant.
5. Understand subscript notation.
6. Use the geometric interpretation and the algebraic definition of rise and run.
7. Find the distance between two points using the Pythagorean Theorem or the distance formula
8. Find the equation of the circle given the center and radius.
9. State the center and radius of a circle given the equation.
10. Recognize a linear equation in two variables.
11. Identify solutions of linear equations in two variables .
12. Graph a linear equation by plotting ordered pairs.
13. Graph horizontal and vertical lines and recognize their equations.
14. Determine the intercepts of a linear equation.
15. Graph a linear equation using the intercepts.
16. Find the slope of a line given two points.
17. Define positive slope , negative slope, zero slope, and undefined slope.
18. Graph a line given a point and the slope.
19. Graph parallel and perpendicular lines and find their slopes
20. Find the equation of the line given a point on the line and the slope.
21. Use the point-slope form of the equation of a line.
22. Find the equation of the line given two points on the line.
23. Use the slope-intercept form of the equation of a line
24. Find the equations of horizontal or vertical lines.

To study for the exam:

1. review material on the CD
2. in your PAN for each lesson (3.1, 4.1, 4.2)
• review objectives (pages 223-225, 258-259, 279-280)
• read the EXPLAIN sections and do the sample problems for EXPLAIN and EXPLORE (pages 207-221, 241-256, 267-276)
• do the HOMEWORK (pages 226-228, 260-260, 281-282)
• review the APPLY practice problems you have done (pages 229-233, 262-264, 283-285)
• do the EVALUATE practice test (pages 234-235, 265-266, 286) (note: answers to all questions for the EVALUATE practice test may be found at the back of your PAN)

PRACTICE PROBLEMS

1. Consider the points (-4, 3) and (5, 0), and find the slope of the line that joins these two points.

2. Find the rise and the run in moving from the point (-1, 2) to the point (4, -7).
rise=
run =

3. Use the distance formula to find the distance between the points (4, 2) and

4. If a = 8 and b = 15, use the Pythagorean Theorem to find c, the length of the hypotenuse of
the right triangle shown below. 5. What is the equation of the circle whose center is at (2, -4) and whose radius is 5?

6. Circle all of the linear equations in two variables: 7. Circle the points below that lie on the line whose equation is x + 4y = 18. 8. Complete the table for the equation shown. Plot the ordered pairs and draw a line through the
points. 9. Graph the equation 2x + y = 3. 10. Graph the equation x = 2. 11. Find the x- and y-intercepts of the line 2x – 5y = 20.
x-intercept =
y-intercept =

12. Find the x- and y-intercepts of the line 3x + y = 6 and use them to graph the line. 13. Find the slope of the line through the points (2, -3) and (-5, 4).

14. What is the slope of the horizontal line y = 4?

15. Find the slope of a line parallel and perpendicular to the line that passes through the
points (2, -3) and (5, 9).
Parallel =
Perpendicular =

16. Graph the line with the slope of 3 that passes through the point (-1, 2). 17. Find the equation of the line that passes through the point (-4, 1) and has a slope
m =1/2. Write the equation in the form of y = mx + b.

18. Find the equation of the line that passes through the points (7, 2) and (-5, 4).

19. State the slope and the y-intercept of the line y = (-1/3)x – 7.

slope =
y-intercept =

20. Find the equation of the vertical line that passes through the point (-5, 7).   Prev Next

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