Linear Relationships
Find the equation of a line between the points (1, 5) and (-1, 11).
y=3x+8
Solve for x: x + 5 = 24
x = 19
a^2+7a+6=0
(a+6) (a+1)
The relationship between volume of landfill and time when the volume doubles every 3 years. What type of relationship is this?
Exponential because the volume is multiplying by 2 every 3 years.
Solve for 'a' in 4a+2+6=x
a = x+2
What is the slope of a line 12x+10=2y-4
6.
x: -5x = 35
x = -7
b^2+4b+4=0
(b+2)^2
The relationship between the number of bacteria and time when a culture of 6,000 bacteria is reduced by 50% every 4 hours. Why is it exponential?
Exponential because the number of bacteria is dividing by 2 every 4 hours (the same as multiplying by 0.5 every 4 hours)
Solve for B in 2b+a+1-b+3=0
b=a+2
The train fee goes up per every stop. 3 stops at 6.50, 7 at 12.50. What is the initial fee?
2 dollars.
Simplify the expression 2(x + 3) = 0
x = 3
h^2+10h+9=0
(h+9) (h+1)
Draw what y=x^2+3
(See Picture)
Solve for b in 2a-5b+3+a-2=0
b=3a+1
A wrestler is on a diet. W(t) represents his weight in kilograms. 80 is his weight now. What is his starting weight?
w(t)=80 Kg.
-3(12x) = 36
x = -1
x^2-36
(x+6) (x-6)
A new car costs $23,000. The value decreases by 15% every year. Write an exponential model to represent the car's value after t years.
y=23,000 (.85)^t
Solve for x in 9x+2+3-4x
x=-1
Julia takes 40 minutes to walk 5 kilometers. She takes 52 minutes to walk 7 kilometers. How long does she walk for 1 kilometer?
6 minutes.
Simplify the expression -4(4x + 5)
-16x - 20
q^2+12q+32=0
(q+8) (q+4)
(See Picture)
y=(-x+3)^2+1
Solve for a in 2a-4b+5-4a-4=0
a=-2b+2