Introduction to Basic Algebra Tools
3rd
Grading Period
Topics in Chapter 6 (Analyzing Linear Equations) include determining the slope of a line by looking at a graph and by using the slope formula; writing linear equations in Standard Form (Ax + By = C) and Slope-Intercept Form (y = mx + b); graphing linear equations given: 2 points, 2 points and the slope, or any type of linear equation including using x- and y-intercepts; recognizing parallel and perpendicular lines by comparing the slope of an equation.
Tip: Knowledge of graphing points (coordinates) on a coordinate plane, solving for a specific variable and being able to rearrange equations from one form to another are skills that will be very helpful when graphing linear equations. Most of the time you can graph a line simply by gathering small pieces of information from the equation! You just have to know what type of equation you’re given (standard form or slope-intercept form).
Examples of Standards:
Slope: Determine the slope of a line given (1, 9) and (-3, 16).
Standard Form: Find an equation of a line through (0, -3) with slope 2/5.
Slope: What is the slope of the graph 4x + 5y = 10?
Slope-Intercept: Write the slope-interept form of the line with m= -2/7 and b=3.
Parallel Lines: What is the slope of a line parallel to the equation 3x + 2y = 18?
Graphing: Graph 6x – 4y = 12
More Glencoe sample problems are available online:
More Glencoe sample problems are available online:
Glencoe
Chapter Test, Chapter 6
Do you want to take a Douglass Chapter 6 practice
test?
Douglass Chapter Test, Chapter 6
Topics in Chapter 7 (Solving Linear Inequalities) include
solving inequalities using addition, subtraction, multiplication and division
(similar to solving linear equations in Chapter 3) and graphing their solutions
on a number line; graphing solutions of a compound inequality (and/or;
union/intersection) on a number line; graphing solutions of open sentences that
involve absolute values; graphing inequalities involving two variables in a
coordinate plane.
Tip: This chapter is similar to chapter 3, so you need to know how to solve equations for a variable. Knowledge of the number line is also helpful. Be aware that inequalities don’t have just one answer, they have a range of answers and all of them make the inequality statement true. Also remember that even though you may graph the “boundary” of an inequality on a coordinate plane as a line (dashed or solid), you need to shade the side of the coordinate plane that would make the inequality true.
Examples of Standards:
Solving: Solve m - 13 £ 12
Solving: Solve 5(2c-3) £ 7c + 6
Solve & Graph: n + 2 <11 and n – 6 > 8
Solve & Graph: | x + 7 | £ 10
Graph on a CP: y < -2x + 2
More Glencoe sample problems are available online:
More Glencoe sample problems are available online:
Glencoe
Chapter Test, Chapter 7
Do you want to take a Douglass Chapter 7 practice
test?
Douglass Chapter Test, Chapter 7
Topics in Chapter 8 (Solving Systems of Linear Equations & Inequalities) include graphing systems of linear equations on a coordinate plane to find the solution (as an ordered pair (x, y)); solving systems of equations using methods such as substitution, elimination using addition and subtraction, elimination using multiplication then addition; an graphing systems of inequalities on a coordinate plane.
Tip: Knowing how to graph a line is simply the first step in this chapter! After that, you need to determine where the two lines cross (if they do) so that you can state the solution. Again, recognizing the “forms” of the equations given to you will allow you to gather specific pieces of information in order to graph a line quickly. However, since graphing is not always an accurate way of finding solutions, you need to know how to solve for a specific variable, use your substitution skills, and also multiplication to eliminate certain terms of your equations.
Examples of Standards:
Solve the system by substitution: x = 4y
x + 2y = -6
Solve the system by addition: x + y = 6
x – y = 2
Use multiplication and elimination: 2x + 5y = 3
-x + 3y = -7
Solve by graphing on a CP: y ³ 2x
y > x – 2
More Glencoe sample problems are available online:
More Glencoe sample problems are available online:
Glencoe
Chapter Test, Chapter 8