Lines & Slope
Find the slope between
(−3, 1) and (3, 7)
1
Solve: x² − 9 = 0
x = ±3
What percent growth is represented by: 1.08
8%
Solve:
x + y = 10
x − y = 2
(6,4)
Simplify:
2x + 3x
5x
A line has slope −3 and passes through (3,5).
What is the equation?
y = −3x + 14
Factor: x² − 5x − 24
(x − 8)(x + 3)
A population starts at 200 and grows 12% per year.
f(t) = 200(1.12)^t
Solve:
2x + y = 7
x + y = 5
(2,3)
Simplify:
3(2x − 5)
6x − 15
A line passes through (2,4) and (6,12).
What is the y-intercept?
−2
Find the vertex of: y = (x − 2)² − 5
(2, −5)
Find the horizontal asymptote of
y = 5(2)^x − 7
y = −7
3x + 4y = 26
x + 2y = 12
Find x + y
7
Simplify:
3(2x − 5) − 4(x + 7)
2x − 43
Two lines are perpendicular.
One has slope 4/3.
What is the slope of the other?
−3/4
How many real solutions does this have?
x² + 4x + 10 = 0
0
(b² − 4ac = −24)
A quantity halves every 4 hours.
Initial value = 80.
Write the model.
f(t) = 80(0.5)^(t/4)
5x + 4y = 13
−2x + 3y = 4
Find y
2
Multiply:
(2x + 6)(4x − 5)
8x² + 14x − 30
A line passes through (1,3) and is parallel to
6x + 2y = 20
Find the equation.
Slope = −3
y = −3x + 6
Solve: 2x² − 7x + 3 = 0
x = 3
x = 1/2
A bacteria culture is modeled by
P(t) = 400(1.15)^(t/3)
What does t/3 mean?
The population multiplies every 3 time units
A system represents:
2x + 4y = 10
x + 2y = 5
How many solutions?
Infinite
(same equation)
Solve:
|x − 34| = 47
x=81
x=−13