OBJECTIVE:

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6-5 Graphing Linear Equations
OBJECTIVE You will graph a line given any linear
equation.
In the last chapter, we learned how to graph
lines. Basically, you were taught to (1)
solve the linear equation for y, (2) choose
three x-values (domains) (3) plug those values
into the solved equation from (1), (4) plot the
resulting ordered pairs, and (5) draw the line
through those points with arrows on the ends. In
this section, we will look at two other ways to
graph lines. Neither method is more accurate. The
first you will use most of the time. The second
method is used only when an equation is already
in standard form.
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6-5 Graphing Linear Equations
EXAMPLE 1 Graph y - 1 3(x 2).
(1) Solve the equation for y to get it in
slope-intercept form.
y - 1 3x 6
Distribute the 3.
Add 1 to both sides.
y 3x 7
(2) Identify the slope and y-intercept.
(3) Plot the intercept.
(4) To get the next point, use the slope (in
fraction form) which says to go up 3 and right
one.
(5) Draw the line through the two points.
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6-5 Graphing Linear Equations
EXAMPLE 2 Graph
(1) Solve the equation for y to get it in
slope-intercept form.
Multiply both sides by 2.
(2) Identify the slope and y-intercept.
(3) Plot the intercept.
(4) To get the next point, use the slope which
says to go down 3 and right two.
(5) Draw the line through the two points.
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6-5 Graphing Linear Equations
The next example shows an easier way to graph
linear equations ONLY IF THEY ARE ALREADY IN
STANDARD FORM.
EXAMPLE 3 Graph 2x 5y 20.
(1) Find the x-intercept.
2x 5(0) 20 2x 20 x 10
(2) Plot it.
(3) Find the y-intercept.
2(0) 5y 20 5y 20 y 4
(4) Plot it.
(5) Draw the line through the two points.
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6-5 Graphing Linear Equations
You have now learned three different ways to
graph linear equations.
The first way was creating a chart, choosing
domains, finding ranges, plotting three points,
and drawing a line. You do not need to use this
method any more. The second way only works when
the equation is in standard form. Find the
intercepts, plot them, then draw the line. The
third way will be your most-used method. (1)
Solve the equation for y. (2) Determine your
slope and y-intercept. (3) Plot the
y-intercept. (4) Use the slope to plot the next
point on the graph. (5) Draw the line through
those two points. Now for a tricky example.
Hint its one long sucker.
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6-5 Graphing Linear Equations
EXAMPLE 4 Graph
(1) Solve the equation for y.
(2) Identify the slope and y-intercept.
(3) Plot the intercept. Because of the fraction,
you have to plot in-between the grid lines. Just
do your best.
(4) Go down eleven and right three to get next
point.
(5) Draw the line through the two points.
8x - 6y 30x - 50
- 6y 22x - 50
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6-5 Graphing Linear Equations
HOMEWORK
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