Unit B: Linear Equations B.1 Introduction to Linear Equations and Slope
Dec 29, 2015
Unit B: Linear Equations
B.1 Introduction to Linear Equations and Slope
What is a linear equation?
• An equation that has no operation other than addition, subtraction, and multiplication of a variable by a constant.
• The variables may not be multiplied together, or appear in a denominator.
• Do not contain variables with an exponent other than 1.
Examples and non-examples
Examples• 5x-3y=7
• X=9
• 6s=-3t-15
• Y=1/2 x
Non-Examples• 7a+4b2 = -8
• X+xy=1
• Y=1/x
Example 1
• State whether each is a linear equation. Explain.
• Y=10-5x• Y=x4-5• H=2xy
What is a linear equation?
• The SOLUTIONS to a linear equation are the values of (x,y) that make the equation balance.
• To find solutions to any equation, plug in whatever you want to x, then solve for y.
• How many solutions can you find to the equation y=2x?
• The solutions can be represented by using the order pairs, or you can draw them on a graph.
• Let’s draw the solutions to y=2x on the graph.
Intercepts• Intercepts are the points on a graph where
the line passes through the x- and y-axis. • What would the x- and y-intercepts of this
graph be?
Slope
• The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates.
• Basically, it represents how steep the line is.
• There are two ways we can find slope.
Rise over Run
• When given a graph, it is pretty easy to find the slope of the line.
• 1. Find two points where the x and y are whole numbers.
• 2. Count how many up or down you have to go, then count how many left or right you have to go to get from one point to another.
Example 2
• Find the slope of this line.
• Remember: Rise OVER run
Example 3
• Find the slope of this line.
• Remember: Rise OVER run
• Pos/neg zero undefined
Finding Slope Using Ordered Pairs
• Use the formula:
• m= y-y/x-x
• Where the first y and x must come from the same ordered pair.
Example 4
• Find the slope of the line that passes through the points (-3,2) and (1, -4).
• Find the slope of the line that passes through the points (-4,-3) and (2,1).
Equations of Lines
• The equation of a line in slope-intercept form is
• Y=mx+b where m is the slope and b is the y-intercept.
• Example:What is the slope and the y-intercept of Y=2x+4?
Example 5
• Write the equation of a line that has a slope of 3 and a y-intercept of -1.
Example 6
• What is the slope and y intercept of the line 2x+4 = 2y?
• What is the slope and y-intercept of the line 12x-4y=8x?
Example 7
• Write the equation of the line that goes through (3,1) and (2,2).
• Write the equation of the line that goes through (-1,-1) and (4,5).
Graphing Lines Given the Equation
• To graph a line, put it in slope-intercept form (solve for y).
• Then, graph the y-intercept.• Lastly, use the slope to graph another point.
Example 8
• Graph the line x-y=6.
Example 9
• Write the equation of the line shown below.
Equations of Vertical and Horizontal Lines
• Horizontal: Remember HOY– H=horizontal– 0=zero slope=– Y=# is the equation
• Vertical: Remember VUX– V=vertical– U=undefined slope– X=# is equation
Example 10
• Graph the line that has an undefined slope and passes through (1,2).
• Graph the horizontal line that passes through (0,1).