2.3 Quick Graphs of Linear Equations
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1 2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11
2 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. A line with this equation has a y-intercept at (0, b) and a slope of m. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 2 / 11
3 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. A line with this equation has a y-intercept at (0, b) and a slope of m. Standard Form The standard form of a linear equation is in the form Ax + By = C where A, B, and C have to be integers. A and B both cannot be zero either. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 2 / 11
4 Graphing Lines 1 Make sure that the graph is linear, first of all. These means that there should be no exponents. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 3 / 11
5 Graphing Lines 1 Make sure that the graph is linear, first of all. These means that there should be no exponents. 2 Solve the equation for y. Make sure that the equation is in the form y = mx + b Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 3 / 11
6 Graphing Lines 1 Make sure that the graph is linear, first of all. These means that there should be no exponents. 2 Solve the equation for y. Make sure that the equation is in the form y = mx + b 3 Identify and plot the y-intercept. This will be located at the point (0, b). Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 3 / 11
7 Graphing Lines 1 Make sure that the graph is linear, first of all. These means that there should be no exponents. 2 Solve the equation for y. Make sure that the equation is in the form y = mx + b 3 Identify and plot the y-intercept. This will be located at the point (0, b). 4 Use the slope to find a second point. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 3 / 11
8 Graphing Lines 1 Make sure that the graph is linear, first of all. These means that there should be no exponents. 2 Solve the equation for y. Make sure that the equation is in the form y = mx + b 3 Identify and plot the y-intercept. This will be located at the point (0, b). 4 Use the slope to find a second point. 5 Connect the points with a straightedge to create your line. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 3 / 11
9 Graphing with the Slope-Intercept Form Example Graph y = 1 2 x 1. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 4 / 11
10 Graphing with the Slope-Intercept Form Practice Graph y = 3 5 x 4. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 5 / 11
11 Graphing when in Standard Form Example Graph 3x 2y = 6. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 6 / 11
12 Graphing when in Standard Form Practice Graph 2x + 5y = 10. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 7 / 11
13 Horizontal and Vertical Lines The graph of y = c is a horizontal line through (0, c). This is because every point on that line has a y-coordinate of c. The graph of x = c is a vertical line through (c, 0). This is because every point on that line has a x-coordinate of c. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 8 / 11
14 Graphing Horizontal and Vertical Lines Practice Graph y = 5. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 9 / 11
15 Graphing Horizontal and Vertical Lines Practice Graph x = 2. Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 10 / 11
16 2.3 Quick Graphs of Linear Equations Assignment Graphing Lines Worksheet (available online as well) Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 11 / 11
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