Lesson Module: Linear Equations in Two Variables

Objective: Students will be able to solve linear equations in two variables and graph them on a coordinate plane.

Materials: - Graph paper - Pencils - Rulers - Calculator (optional)

Introduction: Linear equations in two variables are equations that can be graphed on a coordinate plane. They are called linear because they form a straight line when graphed. In this lesson, we will learn how to solve linear equations in two variables and graph them on a coordinate plane.

Instruction: 1. Definition of Linear Equations in Two Variables - A linear equation in two variables is an equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. - The slope of a line is the ratio of the change in y to the change in x. It tells us how steep the line is. - The y-intercept is the point where the line crosses the y-axis.

1. Solving Linear Equations in Two Variables - To solve a linear equation in two variables, we need to find the values of x and y that make the equation true. - We can do this by substituting values for x and y and solving for the other variable. - For example, let’s solve the equation y = 2x + 3 for x when y = 7. - We substitute y = 7 into the equation and get 7 = 2x + 3. - Then we solve for x by subtracting 3 from both sides and dividing by 2. We get x = 2.

2. Graphing Linear Equations in Two Variables - To graph a linear equation in two variables, we need to plot two points on the coordinate plane and draw a line through them. - We can find the y-intercept by looking at the equation and seeing where the line crosses the y-axis. - We can find another point by using the slope. The slope tells us how much the line goes up or down for every unit it goes to the right. - For example, let’s graph the equation y = 2x + 3. - We start by plotting the y-intercept, which is (0, 3). - Then we use the slope, which is 2, to find another point. We go up 2 units and to the right 1 unit from the y-intercept and get the point (1, 5). - We connect the two points with a straight line to graph the equation.

Practice: 1. Solve the equation y = 3x - 2 for x when y = 7. 2. Graph the equation y = -2x + 4 on a coordinate plane. 3. Solve the equation 2y - 4x = 8 for y when x = 3. 4. Graph the equation 4x - 2y = 8 on a coordinate plane.

Assessment: 1. Give students a set of linear equations in two variables and have them solve for x or y. 2. Give students a set of coordinate planes with equations graphed on them and have them identify the slope and y-intercept of each equation.

Conclusion: Linear equations in two variables are important in many fields, including science, engineering, and economics. By learning how to solve and graph these equations, we can better understand the relationships between variables and make predictions about the future.