Slopes & Graphs
What is the slope of a line that rises 6 units for every 3 it runs?
m = 2
Write slope-intercept form with m = 4 and b = –1.
y = 4x – 1
What’s the slope of a line parallel to y = 3x + 1?
3
What is the parent linear function?
f(x) = x
A cell plan costs $15 + $0.10 per text. Write an equation.
C = 0.10x + 15
Find the slope of the line passing through (2, 3) and (8, 9).
1
Write the equation of the line through (0, 4) with slope –½.
y = –½x + 4
What’s the slope of a line perpendicular to y = –¼x + 7?
4
What happens to f(x)=x when it becomes f(x)=3x?
Steeper
Which shows causation?
(A) Hours worked & pay, (B) Ice cream & sunburns, (C) Shoes & GPA.
A
Find the x- and y-intercepts of y = –2x + 6.
x = 3, y = 6
A line passes through (3, 2) and (6, 8). Find the equation.
y = 2x – 4
Write an equation of a line parallel to y = –2x + 5 through (0, 2).
y = –2x + 2
If y varies directly with x, y = 12 when x = 3. Find y when x = 8.
y = 32
Which function best models this situation:
A rental company charges a $50 flat fee plus $25 per hour to rent equipment?
C=25x+50
A line passes through (0, 5) and (10, –5). What is the rate of change?
m = –1
Write in point-slope form: slope = 3 through (–2, 5).
DO NOT SOLVE FOR Y
y – 5 = 3(x + 2)
Write an equation of a line in point slope form perpendicular to y = ½x – 3 through (2, 1).
y – 1 = –2(x – 2)
How does g(x)=f(x-3) differ from f(x)=x?
Shifted 3 units to the right
A survey shows a connection between shoe size and reading ability in children.
Is this association or causation? Explain your reasoning.
Association — older children tend to have both bigger feet and stronger reading skills, but one does not cause the other.
Compare slopes: which is steeper, y = ½x + 1 or y = –3x + 5?
y = –3x + 5
Write in slope intercept form: slope = –⅔ through (3, 9).
y= -2/3x+11
How can you tell if two lines are parallel or perpendicular from their slopes?
Parallel → same slope; Perpendicular → opposite reciprocals.
Describe the transformations from f(x)=x to f(x)=2x + 3.
Steeper and shifted up 3
Explain association vs. causation with an example.
Association: related; Causation: one causes the other.