Graphing Linear Equations Chapter 7 Section 2 Graphing Linear Equations

Learning Objective Graph linear equation by plotting points. Graph linear equation in the form of ax + by = 0 Graph linear equations using the x- and y-intercepts. Graph horizontal and vertical lines. Study applications of graphs. Key Vocabulary: linear equation in two variables, graph of an equation, x-intercept, y-intercept, horizontal line, vertical line.

Graphing Linear Equations There are two methods that can be used to graph linear equations. Graph by plotting points Graph by the x-intercept (x, 0) and y-intercept (0, y) Solve for y. (get y by itself on the left side of the equal sign) Select a value for x. substitute the value in the equation and find y. Record the ordered pair (x,y) Repeat for 2 more ordered pairs. Plot the pairs, they should be collinear. Draw a straight line, with arrow on both ends) through the three points The scale of your axes will result in a different look.

Graph Linear Equations by Plotting Points Example: y = 2x + 1 y = 2x + 1 y = 2(0) + 1 y = 1 y = 2x + 1 y = 2(1) + 1 y = 3 y = 2x + 1 y = 2(2) + 1 y = 5 x y 1 3 2 5 y (2,5) (1,3) (0,1) x (0,0)

Graph Linear Equations by Plotting Points Example: 2y = 3x – 4 y (4,4) x y -2 2 1 4 (2,1) x (0,0) (0,-2)

Graph Linear Equations in the form of ax + by = 0, always passes through the origin Example: 2x + 3y = 0 y x (0,0) x y 3 -2 6 -4 (3,-2) Choose values of x that are multipliers of 3 and the denominator will divide out. (6,-4)

Graph Linear Equations using the x- and y-intercept x-intercept, point at which the graph crosses the x axis (x, 0) y-intercept, point at which the graph crosses the y axes (0, y) xy-intercept , point at which the line crosses at the origin (0,0) (0,2) y-intercept x (0,0) (-2,0) x-intercept

Graph Linear Equations using the x- and y-intercept Find y-intercept (0, y) by setting x = 0 and find the value for y. Find the x-intercept (x, 0) by setting y = 0 and find the value for x. Find a checkpoint by selecting a non-zero number for x and find y. Plot y-intercept, x-intercept and the checkpoint, should be collinear (a straight line) Draw line with arrows on each end.

Graph Linear Equations using the x- and y-intercept Example: 4y = 8x + 4 y (1,3) x y 1 -1/2 3 (0,1) (-1/2,0) x (0,0)

Graph Linear Equations using the x- and y-intercept Example: 3x + 5y = 9 y x y 9/5 3 1 4/3 6 -7 -3 8 (9/5,0) (1,4/3) x (0,0) (0,3)

Graph Linear Equations using the x- and y-intercept Example: y = 10 x + 20 y (1,30) (0,20) x y 20 -2 1 30 x (-2,0) (0,0)

Graph Horizontal Lines The graph of an equation of the form y = b is a horizontal line, whose y-intercept is (0,b) Example: y = -2 (0,-2) Means x = 0 y x (0,0) (0,-2)

Graph Vertical Lines y x The graph of an equation of the form x = a is a vertical line, whose x-intercept is (a,0) Example: x = 4 (4, 0) Means y = 0 y x (0,0) (4,0)

Remember It is not necessary to always solve for y first. However, it can be helpful in finding values for x. Pick values that are easy to work with, such as 0 and 1 when possible. Try to pick values that will divide out a fraction when possible. Every point on a graph represents an ordered pair solution to the equation of the graph.

HOMEWORK 7.2 Page 439: #21, 23, 25, 29, 35, 45, 47, 50, 61, 65, 67