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AlgebraAlgebra
4.6 4.6
Slope Intercept FormSlope Intercept Form
And Parallel LinesAnd 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 FormSlope-Intercept Form
y = mx + b
slope y-intercept
where the line crosses the y axis
riserun
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
35
4 xy
Now let’s graph this equation.
Graph the y-intercept
.(0,-3)
x
y
The y intercept of the line is -3.Plot the point (0,-3) on the y axis.
35
4 xy
Using the slope to find more points
. (10,5)
. (5,1)x
y
The slope of the line is or
Rise 4Run 5
35
4 xy
5
4
From the y intercept of (0,-3) rise 4, run 5, plot, repeat. Then connect for the line.
.(0,-3)
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
x
y
y = 5
y = 3
y = -2
y = -6
Horizontal lines areall parallel to each other.
Horizontal lines all have a slope of 0.
Vertical Lines
x
yx = 5x = 3
x = -2x = -6Vertical lines areall parallel to each other.
Vertical lines all have a slope that is UNDEFINED.
x
y
Sloped lines areall parallel to each other if they have the same slope.
y = 2x - 5
y = 2x - 2
y = 2x + 1
y = 2x + 4Sloped Lines
x
y
Sloped lines areall parallel to each other if they have the same slope.
y = -½x + 4
Sloped Lines
y = -½x
y = -½x -3
y = -½x - 4
Check for Understanding
Which of the following lines are parallel? (Hint: convert to slope-intercept form and compare slopes)
a) 3y = -9x – 5 b) 2y – 6x = -5c) 12x + 4y = 1
Answer: Lines a and c are parallel. They both have a slope of -3.
Homework
pg. 245 #46-55, 60-61, 66-68pg. 247 Quiz 2 all
