340 likes | 463 Views
Graphing Linear Equations. Graphing Linear Equations. Linear equation: an equation with two variables that are both to the first power . Ex. x + y = 3 The graph of a linear equation will always be a straight line.
E N D
Graphing Linear Equations • Linear equation: an equation with two variables that are both to the first power. Ex. x + y = 3 • The graph of a linear equation will always be a straight line.
Previously, you’ve solved equations that contain just one variable. For example, let’s solve: 2x + 3 = 7
Linear equations have an infinite number of solutions. • When we solve a linear equation, we get a list of ordered pairs. • The graph of all of the ordered pairs creates a straight line.
Horizontal and Vertical Lines • Sometimes, the graph of an equation is a horizontal or a vertical line. • If our equation only contains a “y”, then our graph is a horizontal line. • If our equation only contains an “x”, then our graph is a vertical line.
Example y = 3
Example x = 3
Examples For each of the following linear equations: • Find four ordered pair that complete the equation • Plot the ordered pairs on a coordinate plane • x + y = 6 2) y = x + 1 3) x = 4
x + y = 6 Ordered Pairs
Y = x + 1 Ordered Pairs
x = 2 Ordered Pairs
Slope • Slope: A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill. • Think of a road going uphill (or downhill). The steepness of the road is the slope.
The slope we are studying is associated with the graph of a line.
Vertical ChangeHorizontal Change This ratio is also known as Rise Run
Now that we have our line lets find its slope. Remember we are finding the following ratio: Vertical or Rise Horizontal Run
Vertical RiseHorizontal Run 3 4
The slope is… 1 2
The slope is… • Black line 3 • Red Line 1 • Blue Line -1/2
The slope is… • Orange line 0 • Green Line Undefined
Let’s go back to our first example. • Graph the line that goes through (3,2) and (-1,-1)
Equation (3,2) and (-1,-1)