Download 3.6

Goals:
1. Recognize slope-intercept
equation of a line
The PointPoint-Slope
Equation of a Line
2. Use the slope-intercept equation
to graph a line.
For m and b any real numbers, and
x and y variables,
Example: The line
y=
y = mx + b
is the slope intercept equation for a
line with slope = m and y-intercept
at the point (0, y)
The slope and y-intercept is enough
information to graph a line. First, place the yintercept on the graph. Since slope = rise
2
x +1
5
2
has a slope, m = 5 , and a y-intercept at
(0, 1).
If slope is a whole number, divide by 1 to get
rise
.
run
run
you can find another point on the line using
the slope, then connect the points.
y=
y = 3x - 1
2
x +1
5
1
Recall that the fractions
−a
a
a
=
=−
b
−b
b
1
y = − x+7
3
are equivalent. So if slope is negative,
then either rise or run (but not both!)
needs to be in the negative direction.
If an equation for a line is not
already in slope-intercept form, you
can isolate the y variable using the
multiplication and addition
principles.
Example: Rewrite in slope-intercept
form:
4x – 2y = 10
Slopes of Parallel Lines:
Lines are parallel if they have the same slope.
Slopes of Perpendicular Lines:
Lines are perpendicular if the product of their
slopes is -1.
y = 2x + 2
Example:
Which lines are parallel?
Perpendicular?
4 x − 2 y = 10
y = 2x + 2
2 x + 4 y = 12
2x + 4y = 12
4x – 2y = 10
2