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Graphing and Writing
Equations of Lines
(2-4)
Objective: Graph linear equations and
write the equations of lines in slopeintercept and point-slope form.
Forms of Linear Equations
O There are three main forms for the equation
of a line
O Slope-Intercept Form y = mx + b
O m = slope
O b = y-intercept
O Standard Form Ax + By = C
O A, B and C integers
O A > 0, A and B not both 0
O Point-Slope Form y - y1 = m(x – x1)
O m = slope
O (x1, y1) is any point on the line
Graphing Lines
O From slope intercept form
O Determine the y-intercept and plot it on the
graph FIRST
O Determine the slope and use it to find one or
more additional points
O Connect the points. Don’t forget to put
arrows on the ends.
Graphing Lines
O Example:
2
Graph y  x  5
3
O Graph the y-intercept of -5
O From the y-intercept, use
the slope to rise 2 and
run 3. This will give you
a second point. Repeat.
O Use a ruler to connect
the points and create a
line.

y





x










.

.
.


Graphing Lines
O From Standard Form
O Method 1: convert to slope-intercept form
O Method 2: find x- and y-intercepts
Graphing Lines
O Graph 3x + 4y = 24
O x – intercept

O 3x + 4(0) = 24

O y-intercept
O 3(0) + 4y = 24
O 0 + 4y = 24
O y=6
.

O 3x = 24
O x=8
y















.
0
.
x

Graphing Lines
O From point-slope form
O Determine the point (x1, y1)
O Graph the point
O Use the slope to find additional points
O Draw the line
Graphing Lines
O Graph y – 5 = -2(x + 1)
O Rewrite as y – 5 = -2(x - -1)
O The point is (-1, 5)


O Graph the point

.
O The slope is -2/1, so
rise -2 and run 1
y

x















Writing Equations of Lines
O You must be given two pieces of information
to write the equation of a line. This
information can be
O Slope and y-intercept
O Slope and one point
O Two points
O If you are given the graph of a line, you can
get that information from the graph.
Writing Equations
of
Lines
2
y   x 1
3
m
rise 2

run
3
b = -1
b = -1
y = mx + b
2
-1
y = ___x
+ ___
3

rise = -2
run = 3
Writing Equations of Lines
O Write the equation of a line with slope -3
and one point at (-5, 2)
O When given the slope and one point, it is
O
O
O
O
O
easiest to use the point-slope form
y – y1 = m(x – x1)
y – 2 = -3(x - -5)
y – 2 = -3(x + 5) covert to slope-intercept
y – 2 = -3x – 15
y = -3x - 13
Writing Equations of Lines
O When given two points you need to:
O Use the slope formula to determine the slope
O Use the calculated slope and one of the two
points to determine the equation of the line
Writing Equations of Lines
O Write the equation of the line passing
through (-3, 5) and (6, -2).
O Find the slope
m
y2  y1
x2  x1

2  5
6  3

7
9
O Use the slope and one of the two points to
write the equation
O y – y1 = m(x – x1)
7
(x  3)
9
O y  5  7 (x  3)
9
O y 5 
Parallel and Perpendicular
Lines
O Parallel lines have the SAME slope
O Perpendicular lines have slopes that are
OPPOSITE RECIPROCALS
Parallel and Perpendicular
Lines
O Find the equation of the line parallel to
3x + 5y = 7 and passing through (10, -2)
O Find the slope of the original line:
O From standard form, slope is –A/B
O The slope of the line above is -3/5, so the slope
of the parallel line is also -3/5
O Use the slope and the point to write the
equation
3
O y  2   (x  10)
5
3
O y  2   (x  10)
5
Parallel and Perpendicular
Lines
O Find the equation of the line perpendicular
to 8x – 2y = 9 and with y-intercept -4
O Find the slope of the line: -A/B = -8/-2 = 4
O The slope of the line perpendicular to the
given line would be  1
4
O Use the slope and the y-intercept to write the
equation of the line
O y  1 x4
4