Finding The Slope of a
Linea Equation
Some forms of
linear equations
• Standard Form ax +
by = c where a, b,
and c are numbers
and x and y are
variables
• Slope-intercept form
y = mx + b where m
is the slope and b is
the y-intercept and x
and y are variables
How do you
find the
slope in
standard
form?
• m = -a/b
• Example 1 –
4x + 2y = 6
m = -4/2 = -2
• Example 2 –
-6x – 2y = 3
m = 6/-2 = -3
For you to
try
Find the slope of
the line whose
equation is
-10x + 2y = 4
Solution
m = 10/-2 = -5
So, the slope of
the line is -5
How to find
the slope of a
line in slopeintercept
form
• The slope is always the
coefficient of x when
the equation is in slope
–intercept form
• Example 1 –
y = 5x – 1
m=5
• Example 2 –
y = -3/5 x + 7
m = -3/5
What if the
equation is
not in
either
form?
• When an equation is not
in either form, rearrange
the terms so that it is in
either standard form or
slope-intercept form
Example 1 –
5x = -2y + 4
Change the equation to
standard form by
Examples
Example 1 –
5x = -2y + 4
Change the equation to
standard form by bringing
“y” to the same side as
“x” using inverse
operations
5x = -2y + 4
+2y +2y
5x + 2y = 4
So, m = -5/2
More examples
• Example 2 –
-4y – 3x = 2
Rearrange the “x”
and “y” terms so
that the equation
is in standard form
-3x – 4y = 2
m = 3/-4
For you to
try
• Find the slope of
the line
2x – 4y – 1 = 6
Hint: What can
you do to put
this equation in
standard form?
Solution
2x – 4y – 1 = 6
Add 1 to both sides so
that the equation is
now in standard form
2x – 4y – 1 = 6
+1 +1
2x – 4y
=7
m = -2/-4 = 1/2
Notes
• Parallel lines have the
same slope
• The slopes of
perpendicular lines are
the opposite of the
reciprocals of each
other
Ex/ if lines c and d are
perpendicular to each
other and the slope of
line c is 4, then the
slope of line d is -1/4
Notes
continued
Ex2/ if lines e and f
are perpendicular
to each other and
the slope of line e
is -2/3, then the
slope of line f is
3/2