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TRANSCRIPT
Lesson 4.5
Goal: Write and graph linear equations using slope-intercept form of an equation. Question: How do you write and graph linear equations using slope-intercept form? .
Parallel lines have the same slope.
Slope Intercept Form
y = mx + b “m” is the slope (the ratio of rise to
run) Slope is the change of y over the
change of x. “b” is the y-intercept (where the
line crosses the y-axis)
x
y
31
2 xy
32 xy4
3
2 xy
Given the equation of the line in slope-intercept form y = mx+b.
+2
-1
y-intercept
(0, -3)+2
+3y-intercept
(0, -4)
32
3
xy
+2
+1 22 xy
y-intercept
-3
+2
y-intercept
(0, -2)
(0, 3)
Finding the slope and y-intercept of a line.
slope-intercept formm
b
slope y-intercept
+2+1m = 2
-2
-1 y = 2x + 1
Example 1
y = mx + b1 3
y
2x Add
2x + 5
2 5
Slope-Intercept Form of the Linear Equation
Any linear equation which is solved for y is inslope-intercept form.
y = mx + b
Find the slope and y-intercept of the following linear equations:
1) y = 3x + 4
2) y = -2x - 1
3) y = 5x
4) y = x - 458
5) y = x --29
14
6) y = 6
m = 3 b = 4
m = 2 b = -1
m = 5 b = 0
m = b = -458
m = b =-29
-14
m = 0 b = 6
slope: 4
y-intercept: -1
-4x -4x
- 2y = -4x + 8- 2 - 2 - 2
y = 2x +-4slope: 2 y-intercept: -4
4 4 4
y = ¾ x + 4
slope : ¾
y-intercept: 4
- 6x -6x 3y = -6x – 21
y = -2x – 7
slope : -2
y-intercept: -7
Slope-Intercept Form of the Linear Equation
Write a linear equation in the form y = mx + bgiven the following.
1) m = 2, b = -3
2) m = , b = 5
3) m = , y-int = 2
2
3
3
7
4) m = 0, b = 6
5) m = , b = 0
6) m = 1, b =
1
2
2
3
y = 2x - 3 y = 6
2y x 53
3y x 27
1y x2
2y x3
Example 2
y = -4x + 2
Identify-4 2
Plot0, 2
-4
+1
Checkpoint
y = ½ x + 1
y-intercept: 1
slope: ½
Graph the line which passes through (-2, 1) and has a slope of -3.
x
y
1) Plot the point.Steps
2) Write slope as fractionand count off other points.
m = -3 = -31 -3
+1or m =
3-1
3) Draw line through points.
Graph the line which passes through (3, 2) and has a
slope of .
x
y
1) Plot the point.Steps
2) Write slope as fractionand count off other points.
m =34
+3
+4
or m = -3-4
3) Draw line through points.
34
Graph the line which passes through (-5, 4) and has a
slope of .
x
y
1) Plot the point.Steps
2) Write slope as fractionand count off other points.
m = -32
-3
+2
3) Draw line through points.
-32
Parallel Lines
Graph the following on the coordinate plane.
y x 1
23 y x
1
21
m 1
2b 3
m 1
2b 1
x
y
Parallel lines have the same slope.
Example 3
-3 -2
-6 -6
1
-2 -4
-6 -6
1
-5 -3
-7 -9
7 9
a b
Tell whether the lines below are parallel.
1) 3x + y = 7 y = -3x + 1-3x -3x
y = -3x + 7
m = -3
y = mx + b
m = -3
Lines are parallel because they have the same slope!
Same slope!
Checkpoint
4
3
4
3
22
307
5
7
5
43
144
3
4
3
22
52
c
b
a
m
m
m Lines a and b are parallel.
They have the same slope!