End of Year Review Part 2

Writing the Equation of a Line

100

Write the equation of a line with slope -1/2  and passing through the point (6,3).

y=mx +b

3=(-1/2)(6)+b

3=-3+b

6=b

y=(-1/2)x+6

200

Find an equation of the line with slope=5 and passing through the point (3,13).

y=mx+b

13=5(3)+b

13=15+b

b=-2

y=5x-2

300

Find the equation of a line with slope= (-5/3) and passes through the point (3,-1).

y=mx+b

-1=(-5/3)(3)+b

-1=-5+b

b=4

y=(-5/3)x+4

400

Write the equation of the line passing through the points (8,3) and (4,6).

Slope: change in y/ change in x

Slope=(6-3)/(4-8)=3/-4

3=(-3/4)(8)+b

3=-6+b

9=b

y=(-3/4)x+9

500

Find the equation of the line that passes through points (1,1) and (0,4).

Slope=change in y/change in x

Slope= (4-1)/(0-1)=3/-1

y=mx+b

4=-3(0)+b

4=b

y=-3x+4

Rewriting Equations with More than One Variable

100

Solve for y: 2x+3y-9=0

3y=-2x+9

y=-2/3x +3

200

Solve for y: -3x+5y=-10

5y=3x-10

y=(3/5)x-2

300

Solve for x: y=mx+b

y-b=mx

(y-b)/m=x

400

Solve for r: A=r²

(A)^(1/2)=r

500

Solve for r: V=(4/3)r³

3V=4r³

(3/4)V=r³

((3/4)V)^(1/3)=r

Multiplying Polynomials

100

Multiply: 2x(x-1)

2x²-2x

200

Multiply: -5x(-2x+y)

-5x*-2x+-5x*y

=10x²-5xy

300

Multiply (3x+2)(2x+7)

6x²+25x+14

400

Multiply (x-3)(2x+1)

2x²-5x-3

500

Solve x(2x-4)=(2x+1)(x+5)

2x²-4x=2x²+11x+5

-4x=11x+5

-15x=5

x=5^/-15

x=-1/3

Solving Problems by Writing Equations

100

A bag of coins are all nickles and dimes. If there are 33 coins and the value is $2.40, how many of each kind of coin are in the bag. 

d=number of dimes and n= number of nickles

n+d=33

10d+5n=240

Solve

d=15 and n=18

15 dimes and 18 nickles

200

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. When will they both have the same amount of money in the bank? 

m=amount of money in banks

w=weeks

Nancy: m=435+25w

 Shane: m=875-15w

435+25w=875-15w

Solve: w=11 

11 weeks

300

A rectangle is three times as long as it is wide. The perimeter is 36 cm. Find the length of each side. 

w=width and l=length

w+l=36

3w=l

Solve: w=4.5 and l=13.5

400

The sum of two consecutive odd numbers is 76. Find the numbers.

n=first odd number and n+2=second odd number

n+n+2=76

n=37 and n+2=39

odd numbers are 37 and 39

500

Michael is swimming at a rate of 450 feet in 4 minutes. At that rate, how far will he swim in 15 minutes?

r=d/t

450/4=d/15

d=1687.5 feet

Solving Linear Systems of Equations

100

Solve the following system: 4x+y=8

                                         x=5-y

Subsitution:

4(5-y)+y=8

20-4y+y=8

20-3y=8

-3y=12

y=4

x=5-4

x=1

y=4 and x=1

200

Solve the following system

-2x+y=-7

3x-4y=8

Elimination

4(-2x+y=-7)

    -8x+4y=-18

+    3x-4y=8

______________

-5x+0=-20

x=4

-2(4)+y=-7

-8+y=-7

y=1

x=4 and y=1

300

Solve each system of equations

y=-3x

4x+y=2

Subsitution:

x=2 and y=-6

400

Solve the system of equations:

y=7x-5

2x+y=13

Subsitution:

x=2 and y=9

500

Solve the system of equations

x=-5y-4

x-4y=23

x=11

y=-3