Transcript 4.6 Slope-Intercept Form and Parallel Lines

Algebra
4.6
Slope Intercept Form
And Parallel Lines
You have already learned an
easy method of graphing that
uses only the y-intercept (b)
and the slope (m).
Let’s review . . . .
Slope-Intercept Form
y = mx + b
slope
y-intercept
rise
run
where the line
crosses the y axis
Converting to Slope-Intercept
Form (y = mx + b)
Convert:
4x – 5y = 15
-4x
-4x
-5y = -4x + 15
-5
-5
Converting to Slope-Intercept
Form (y = mx + b)
Convert:
4x – 5y = 15
-4x
-4x
-5y = -4x + 15
-5
-5
4
y x3
5
Now let’s graph this equation.
Graph the y-intercept
y
4
y x3
5
The y intercept of the line is -3.
Plot the point (0,-3) on the y axis.
.
x
(0,-3)
Using the slope
to find more points
y
4
y x3
5
4
The slope of the line is
5
or
Rise 4
Run 5
.
.
.
(5,1)
(10,5)
x
(0,-3)
From the y intercept of (0,-3) rise 4, run 5, plot,
repeat. Then connect for the line.
Parallel Lines
• Parallel lines in the same plane do not
intersect
• Horizontal lines are parallel to other horizontal
lines
• Vertical lines are parallel to other vertical lines
• Sloped lines (uphill and downhill) are parallel to
each other if they have the same slope
Horizontal Lines
y
Horizontal lines are
all parallel to each other.
y=5
y=3
x
y = -2
y = -6
Horizontal lines all have a slope of 0.
Vertical Lines
Vertical lines are
all parallel to each other.
x = -6
y
x = -2
x=3
x=5
x
Vertical lines all have a slope that is UNDEFINED.
Sloped Lines
y = 2x + 4
y
Sloped lines are
all parallel to each other
if they have the same
slope.
y = 2x + 1
y = 2x - 2
y = 2x - 5
x
Sloped Lines
y
Sloped lines are
all parallel to each other
if they have the same
slope.
y = -½x + 4
x
y = -½x
y = -½x -3
y = -½x - 4
Check for Understanding
Which of the following lines are
parallel? (Hint: convert to slopeintercept form and compare slopes)
a)
b)
c)
3y = -9x – 5
2y – 6x = -5
12x + 4y = 1
Answer: Lines a and c are parallel.
They both have a slope of -3.
Homework
pg. 245 #46-55, 60-61, 66-68
pg. 247 Quiz 2 all