Graphing Linear Equations
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- Derrick Parrish
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1 Graphing Linear Equations A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
2 What am I learning today? How to graph a linear equation or inequality How will I show that I learned it? Graph a linear equation or inequality in slopeintercept or standard form
3 Vocabulary Solution Set the set of coordinates that provide solutions to a 2 variable equation, represented by a graph on a coordinate plane. X Intercept where the graph crosses the x axis. The x value when y = 0. Y Intercept where the graph crosses the y axis. The y value when x = 0. Slope the rate of change between two points represented by.
4 INB "Graphing Linear Equations" Slope Intercept Form for Graphing a Line y = mx + b or f(x) = mx + b
5 Graphing from slope intercept form: 1. Put your b on the y axis; this is your beginning. 2. Make m a fraction if it is a whole number by putting it over 1. From your b, move up or down by the top number, move right by the bottom number.
6
7
8 Finding slope intercept form from a graph: 1. Identify where the graph crosses your y axis. This is your b value. 2. Find 2 points that are where the graph crosses gridlines. Starting at the left point, count up or down how many units it takes to be even with the other point. This is the top number of your m. Count right how many units it takes to reach the point. This is the bottom value of m. Write as fraction. 3. Replace "m" and "b" in y = mx + b with your values.
9 Standard Form for Graphing a Line ax + by = c
10 Graphing from standard form: (Option 1) 1. Plug 0 in for y to solve for your x intercept. Plot this point. 2. Plug 0 in for x to solve for your y intercept. Plot this point. 3. Connect with a straight edge.
11 2x + 3y = 6
12 4x 2y = 8
13 Graphing from standard form: (Option 2) 1. Solve for y and plot in slope intercept form
14 2x + 3y = 6
15 4x 2y = 8
16 y = # x = # Slope 0 Undefined Type of Line Horizontal Vertical y = 2 x = 2
17 y = 3x y = ( 2/3)x 5
18 Put in slope intercept form and graph. 3x y = 4 2x + 5y = 15
19 Write equations for the following graphs
20 Graphing an Inequality 2 Variable: On a coordinate plane (graph) Solid Line: Dotted Line: Test a point on one side. If it works, shade on same side. If it doesn't work, shade on opposite side.
21 Ex. 1 y < 2x + 4
22 Ex. 2 3x y 5
23 Ex. 3a Write the equation for the following inequality.
24 Ex. 3b Write the equation for the following inequality.
25 Ex. 3c Write the equation for the following inequality.
26 Shaded Region = ALL POSSIBLE SOLUTIONS
27 Tell if the following value is a solution to the inequality. 1. x = 5; x 5 2. x = 3; 2x + 3 > x = 4;
28 Tell if the following coordinate is a solution to the inequality. 1. (2, 4); y > 2x (5, 2); x 2y 1
29 Tell if the following coordinate is a solution to the graphed inequality. 1. ( 3, 3) 2. (4, 0) 3. (1, 2) 4. (3, 2) 5. (0, 3)
30 Use the questions to help graph the inequality. 3x 4y < 8 Slope Intercept Form: Solid or Dotted Line? Test Point: Did it work? Shade on same or opposite side?
31 Graph the following inequalities. y > 2x 3 y ( 1/3)x + 6 y ( 5/2)x 2
32 Put in slope intercept form and then graph the solutions set. 2x + y < 6 x 4y 16 3x + 5y 35
33 Write the equation of the inequality for the following graphs.
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