Unit 3 lesson 5 connexus
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Unit 3 Lesson 5 in the Connexus curriculum focuses on graphing linear equations and inequalities. Here is a step-by-step breakdown of the concepts covered in this lesson:
Step 1: Introduction to Graphing Linear Equations
- The lesson begins with an introduction to linear equations and their properties.
- A linear equation is an equation whose graph is a straight line.
- The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Step 2: Slope-Intercept Form
- The lesson introduces the concept of slope-intercept form, which is y = mx + b.
- In this form, m represents the slope of the line, and b represents the y-intercept.
- The y-intercept is the point where the line crosses the y-axis.
Step 3: Graphing Linear Equations in Slope-Intercept Form
- The lesson provides step-by-step instructions on how to graph a linear equation in slope-intercept form.
- Start by plotting the y-intercept (the point (0, b)).
- Use the slope (m) to find a second point on the line.
- Draw a straight line connecting the two points.
Step 4: Graphing Linear Equations in Standard Form
- The lesson then explains how to graph a linear equation in standard form (Ax + By = C).
- Convert the equation to slope-intercept form by solving for y.
- Once the equation is in slope-intercept form, follow the steps mentioned in Step 3 to graph it.
Step 5: Graphing Linear Inequalities
- The lesson shifts focus to graphing linear inequalities.
- A linear inequality is an inequality in which the solution is a range of points on a graph rather than a single point.
- To graph a linear inequality, first graph the corresponding linear equation (using the steps from earlier).
- Then, depending on whether the inequality symbol is <, >, ≤, or ≥, shade the region above or below the line.
Step 6: Testing Solutions for Inequalities
- The lesson explores how to test solutions for linear inequalities.
- Choose a point in a shaded region and substitute its coordinates into the original inequality.
- If the inequality is true, the point is a solution. If not, it is not a solution.
Step 7: Solving Systems of Linear Equations
- Lastly, the lesson briefly touches on solving systems of linear equations.
- A system of linear equations is a set of equations with multiple variables that share a common solution.
- Methods for solving systems of linear equations, such as graphing, substitution, and elimination, are introduced.
This breakdown should give you a clear understanding of the topics covered in Unit 3 Lesson 5 of the Connexus curriculum.