Linear Functions
Solve the linear system using elimination or substitution
x+3y=1
x=-1
y=4
Write an equation of the line that passes through (-3,-5) and is parallel to the line y=3x-1
y=3x=4
18 + 36 ÷ 3^2
22
Graph the function y=(1/2)^x
TBA
2y+6
2(y+3)
Solve the linear system using elimination or substitution
4x-3y=16
16x+10y=240
x=10
y=8
Determine if these lines are parallel or perpendicular
y=5x-3
x+5y=2
they are perpendicular
Slopes: 5 & -1/5
400
A lab technician is culturing a bacterial sample. The current population is 43,000 bacteria, and the growth rate is 15% per day. How many bacteria will there be in 14 days?
y = a(1 + r)t
y = 43,000(1 + 0.15)14
y = 43,000(1.15)14
y ≈ 43,000(7.0757)
y ≈ 304,255
x^2+4x+3
(x+3)(x+1)
Graph the following function
f(2)=-4 f(5)=-5
TBA
Determine whether lines are parallel
12y=-7x+42
11y=16x-52
no, the slopes are not equal
Slopes:-7/12 & 16/11
289 - (3 x 5)^2
64
The value of houses in Oak Grove goes up by 5% each year. Cara owns a house in Oak Grove that is currently worth $240,000. How much will it be worth in 7 years?
y = a(1 + r)t
y = 240,000(1 + 0.05)7
y = 240,000(1.05)7
y ≈ 240,000(1.4071004)
y ≈ 337,704.1
3y2+12y
3(y2+4y)
f(2)=5 f(6)=3
Slope=-1/2
Y-intercept=6
y=-1/2+6
Write an equation of the line that passes through (4,-5) and is perpendicular to the line y=2x+3
y=-1/2x-3
15 x 12^2 + 150
2,310
Scientists are modeling the spread of a hypothetical virus. In their computer model, there are currently 580 people infected, and the virus is spreading at a rate of 15% each day. How many people will be infected in 11 days?
y = a(1 + r)t
y = 580(1 + 0.15)11
y = 580(1.15)11
y ≈ 580(4.652)
y ≈ 2,698
3u4 − 24uv3
3u(u−2v)(u2+2uv+4v2)
There are fifteen workers employed on a highway project, some at $180 per day and some at $155 per day. The daily payroll is $2400. Let x represent the number of $180 per day workers and let y represent the number of $155 per day workers. Write and solve a linear system to find the number of workers employed at each wage.
x= 3
y=12
Determine which lines, if any, are parallel or perpendicular
4x-3y=2
3x+4y=-1
4y-3x=20
none are parallel
line one and two are perpendicular
8 + (2 x 5) x 3^4 ÷ 9
98
The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963 there were about 41 million acres of Ponderosa pine forests.
A. Write a function that models the number of acres of Ponderosa pine forests in the western United States over time.
B. To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002?
A. p=a(1-r)^t
=41(1-0.005)^t
=41(0.995)^t
B. p=41(0.995)^39=33.7
z3 − z2 − 9z + 9
(z−3)(z+3)(z−1)