Section 2-3
Graphing Linear Equations
If you have two points, you can draw a straight line connecting them.
So, if you have an equation in two variables and you know that equation is
linear (which means its graph is a line), it’s easy to graph it. All
you need to do is find two ordered pair solutions, plot them, and then draw
the line connecting them. (It’s a good idea to do a third point to check
yourself.)
Example:
Graph the equation y = 2x + 3.
Start by choosing some easy points for x, (say 0, 1, and 2), plug
them in, and calculate the corresponding y-values.
| x |
y |
| 0 |
2(0) + 3 = 3 |
| 1 |
2(1) + 3 = 5 |
| 2 |
2(2) + 3 = 7 |
Now, plot the points (0, 3), (1, 5), and (2, 7), and draw the line connecting
them.
Easy!
Sometimes, things can be a little more complicated if the original equation
does not have y alone on one side. In this case, you have to solve
for y first, and then get your ordered pairs.
Example:
Graph the equation 3y + 1 = –4x + 2y.
Start by collecting like terms on one side. Subtract 2y from both
sides.
y + 1 = –4x
Then subtract 1 from both sides.
y = –4x – 1
Now you can plug in some values of x and quickly get the corresponding y-values.
HORIZONTAL AND VERTICAL LINES
Equations of horizontal and vertical lines only have one variable. The equation
x = 4
represents a vertical line which crosses the x-axis at the point
(4, 0). Every ordered pair with 4 as its first coordinate is a solution. (The
equation means “x is equal to 4, and y can be whatever
it wants.”)
Similarly, the equation
y = –3
is a horizontal line which crosses the y-axis at (0, –3).
The point where the horizontal and vertical lines intersect is also easy
to find.
