Math A

Equations and Graphs
 of Straight Lines 

 

When working with straight lines, there are often many ways to arrive at an equation or a graph.   

 

Equation Forms

Slope Intercept Form
(if you know the slope and where the
line crosses the y-axis, use this form)

y=mx + b

m = slope

b = y-intercept
 (where line crosses the y-axis.)

Point Slope Form
(if you know a point and the slope,
 use this form)

m = slope

= any point on the line

 

 

Horizontal Lines

Vertical Lines

y = 3 (or any number)
Lines that are horizontal have a slope of zero.  They have "run", but no "rise".   The rise/run formula for slope always yields zero since rise = 0.
y = mx + b
y = 0x + 3
y = 3
This equation also describes what is happening to the y-coordinates on the line.  In this case, they are always 3.

x = -2 (or any number)
Lines that are vertical have no slope (it does not exist).  They have "rise", but no "run".  The rise/run formula for slope always has a zero denominator and is undefined.

These lines are described by what is happening to their x-coordinates.  In this example, the x-coordinates are always equal to -2.

 

Remember:

If a point lies on a line, its coordinates make the equation true.

(2,1) in on the
line y=2x-3
because 1=2(2)-3
 

The x-coordinate may be called the abscissa.

The y-coordinate may be called the ordinate.

Before graphing a line, be sure that your equation starts with "y=".

To graph 6x+2y = 8
rewrite the equation:
2y=-6x+8
y=-3x+4
Now graph the line using either slope intercept method or chart method. 

 

 

Methods of Graphing a Line

Using slope and y-intercept
y=mx+b

Follow the example 2y = 6x + 4 through this explanation.

1.  Put your equation in "y=" form.
                     y = 3x + 2
2.  The number in front of x is the slope.
     (If necessary, place this number over 1 to
     form a fraction.  This fraction is your
      rise/run.)
                    slope = 3/1       
3.  The "b" value is where the line crosses the
     y-axis.  Be sure to check the sign of this
     number.
                     b = 2
4.  Plot the b value on the y-axis.
                    see graph below
5.  Standing at that point use your rise and run
     values to plot your second point.
     (If rise is positive, move up.  If rise is
      negative, move down.)
     (If run is positive, move right.  If run is
      negative, move left.)
6.  Connect the two points to form the line.

Using a chart 

X Y
-3  
-2  
-1  
0  
1  
2  
3  

Create a chart to hold x and y values from your line.  The x-values usually range from
-3 to +3, but may be any values you wish.

Substitute the x-values into the equation to determine the y-values.
Plot the (x,y) coordinates to graph the line.

While charts often contain more than 2 entries, only two entries are needed to determine a straight line.  A third point should be used to "check" that an error was not made while computing the first two points.
 

 

 

 

 

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Roberts