1. Algebra 1 EOC Summer School
Lesson 8:
Changes to m and b

2. 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

3. Slope-Intercept Form Example
y = ½ x – 3
The slope is ½
The y-intercept is -3
Where do you begin when graphing a line?
How do you use the slope to find the next point on the line?

4. Changing y-intercept Start with the equation y = ¼ x – 2
Write the new equation if the y-intercept is increased by 3 units:
Graph both lines
How do the lines compare?
y = ¼ x + 1
What letter represents the y-intercept?
What is the y-intercept of the original equation?
If the y-intercept is increased by 3 units, what will the new y-intercept be?
How is the slope changed?

5. Describing the effects of changing “b”
What happens to the slope?
What happens to the y-intercept?
What happens to the x-intercept?
Describe the relationship between the 2 lines.
nothing
increases
decreases
How do you know that these lines are parallel?
parallel

6. Changing Slope ¼ times 2 = ½ Start with the equation y = ¼ x – 2
Write the new equation if the slope is doubled:
Graph both lines
How do the lines compare?
y = ½ x – 2
What letter represents the slope?
What is the slope of the original equation?
If the slope is doubled, what will the new slope be?
How is the y-intercept changed?

7. Describing the effects of changing “m”
What happens to the slope?
What happens to the y-intercept?
What happens to the x-intercept?
Describe the relationship between the 2 lines.
steeper
nothing
decreases
How do you know that these lines must intersect?
How do you know that these lines are not perpendicular?
intersecting

8. 3 things about slope… Parallel Lines always have the same slope
Ex: y = 2x – and y = 2x + 3
Perpendicular lines have opposite reciprocal slopes
Ex: y = 2x – and y = - ½ x + 4
Intersecting lines have slopes that are not the same, but are not opposite reciprocal
Ex: y = 3x – and y = 1/3x + 6

9. 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
What is the slope of the original line?
What is the y-intercept of the original line?
What is half of -2?
What is 1 – 4?
y = -1x – 3
Graph the new line:

10. Describe the Changes What happens to the slope?
What happens to the y-intercept?
What happens to the x-intercept?
Describe the relationship between the 2 lines.
Less steep
decreased
decreases
Why are these lines not perpendicular?
intersecting