Week 1 discussion : Systems of linear equations
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The document reviews methods for graphing linear equations, emphasizing the table of values and the slope-intercept form. It details how to transform equations into the y = mx + b format to identify the slope and y-intercept, as well as provides examples for clarification. The document also discusses connecting plotted points to create the graph of the linear equation.
Week 1 discussion : Systems of linear equations
- 1. Lesson 1.1 Review on Graphing Linear Equations Linear Equations can be graphed using table of values. Example 1. Graph x + y = 10 x 3 5 10 y 7 5 y 0 x + y =10 Plot the three points on the coordinate system and connect . x The graph of the linear equation is presented at the right. y Example 2 Graph x - y = 2 x 0 5 2 y -2 3 0 x-y=2 x
- 2. Another way to graph linear equations in two variables is by using the slope-intercept method. Recall that slope is the steepness or inclination of a line. It is the ratio of the vertical change to the horizontal change, the rise over the run. In the form y = mx + b, m is the slope and b is the y-intercept. So, it is important that we transform the given equation into the y form in order to identify the slope and y-intercept. Remember, two points determine a line. Examples: Transform the equations to y - form. Identify the slope and the y- intercept 1. x + y = 24 y = -x + 24 m = -1, b = 24 2. -4x -y = 5 y = -4x - 5 m = -4, b = -5 3. -x + 2y = 8 y= 1x+4 2 m= 1, b=4 2
- 3. Linear equations can be graphed using the slope-intercept form. Let's graph the equation 3x -2y = 4. Follow the steps. • • • • Transform 3x -2y = 4 to y = mx + b y = 3 x - 2. 2 The slope (m) of the equation is 3 and the y- intercept (b) is -2. 2 Locate the y-intercept, -2 at the y-axis. Mark the point associated with this. Starting from the y-intercept move 3 units upward ( rise ) and from this position move 2 units to the right ( run) . Mark this point. ( If the slope is negative move upward then to the left or move downward then to the right) • • Move again from this point using the ratio of the slope. Mark this point. Connect the points with a straight line. Use three points y Run = 2 x Rise=3 y-intercept This is now the graph of 3x - 2y = 4
- 4. Suppose our equation is -3x -2y = 4 Following the steps the graph now of -3x -2y = 4 is presented at the right. What have you noticed on the slope? Did you find any difference between the two equations and their graphs?