Download Day 3 Lesson 8 Notes on Changes to m and b

Algebra 1 EOC
Summer School
Lesson 8:
Changes to m and b
Introduction to Changing m and b
• Remember slope-intercept form of an
equation:
y = mx + b
• m represents the slope
• b represents the y-intercept
Slope-Intercept Form Example
• y=½x–3
• The slope is ½
• The y-intercept is -3
Changing y-intercept
• Start with the equation y = ¼ x – 2
• Write the new equation if the y-intercept is
increased by 3 units: y = ¼ x + 1
• Graph both lines
• How do the lines compare?
Describing the effects of changing “b”
• What happens to the
slope?
nothing
• What happens to the
y-intercept? increases
• What happens to the
x-intercept? decreases
• Describe the
relationship between
the 2 lines. parallel
Changing Slope
¼ times 2 = ½
• Start with the equation y = ¼ x – 2
• Write the new equation if the slope is
y=½x–2
doubled:
• Graph both lines
• How do the lines compare?
Describing the effects of changing “m”
• What happens to the
slope?
steeper
• What happens to the
y-intercept? nothing
• What happens to the
x-intercept? decreases
• Describe the
relationship between
the 2 lines. intersecting
3 things about slope…
1. Parallel Lines always have the same slope
Ex: y = 2x – 5
and
y = 2x + 3
2. Perpendicular lines have opposite reciprocal
slopes
Ex: y = 2x – 3
and
y=-½x+4
3. Intersecting lines have slopes that are not
the same, but are not opposite reciprocal
Ex: y = 3x – 1
and
y = 1/3x + 6
Changing m and b
• The graph of y = -2x + 1 is graphed below.
What is the effect of halving the slope and
decreasing the y-intercept by 4 units?
Write the new equation:
y = -2x + 1
y = -1x – 3
Graph the new line:
Describe the Changes
• What happens to the
slope? Less steep
• What happens to the
y-intercept? decreased
• What happens to the
x-intercept? decreases
• Describe the
relationship between
the 2 lines.
intersecting