Creating Equations
Rewriting Equations
Finding Slope and
y-intercept
y-intercept
Graphing Equations
Solving Systems of Equations
100
Johnny went to Ghirardelli Square in San Francisco wanting to get a box of chocolates for his granny. The tin box it comes in costs $2.50 and each chocolate costs $0.50 each. Create an equation that might represent the total cost of his box of chocolates.
Answers may vary! This is just one example:
T=0.5x+2.5
100
Isolate the y variable in this equation
5+y=28
y=23
100
Identify the slope and y-intercept of the following equation
y=2x+3
slope: 2
y-intercept: 3
100
Graph the following equation:
y=2x+4
100
Solve the following system of equations by substitution:
{(y=2x),(2x+3y=16):}
(2, 4)
200
Jimmie went to the Blue Store with 20 dollars in his pocket to buy breakfast. He likes to get waffles and drumsticks, but he wasn't totally sure how much he wanted to buy. If waffles cost $6 each and drumsticks cost $1 each, create an equation that represents how much Derrick could buy at the Blue Store that day.
Answers may vary! Here is one acceptable example:
20=6w+d
200
Isolate the x variable in this equation.
2y+x=4
x=4-2y
200
Identify the slope and y-intercept of the following equation
y=-3+4x
slope: 4
y-intercept: -3
200
Graph the following equation:
y=-3x+4
200
Solve the following system of equations by elimination:
{(y=-2x+4),(y=2x+8):}
(-4,12)
300
Britney wants to go to Six Flags with her family for her 15th birthday. Entrance to the park is $50 for adults and $30 for kids under 17. First, create an equation that represents the total cost of her family's entrance into the park. Then, figure out how much it would cost for her family to enter if both of her parents are going and she has three siblings under 17.
First,
T=50a+30k
Then,
a=2 and k=4
T=50(2)+30(4)=100+120=220
300
Isolate the y variable in this equation
2y+2x=8
y=4-x
300
Identify the slope and y-intercept of the following equation
y=-24x
slope: -24
y-intercept: 0
300
Graph the following equation AND identify the slope and y-intercept:
-2x+y=5
The slope is 2 and the y-intercept is 5.
300
Solving the following system of equations using substitution:
{(y=x+4),(2x+2y=20):}
(3,7)
400
Felicia wants to get healthier with her family so she convinced her mom to get gym memberships for everyone in her family. Gym memberships cost $20 per month, per person. For families, there is a $10 rebate per month. First, create an equation that could represent the monthly cost of the family's memberships if she has two siblings and one parent. Then, figure out how much a yearlong membership at this gym would cost for Felicia's family.
First, the monthly cost can be represented by
M=20m-10
Then the yearly cost for Felicia's family would be
M=$20(4)-$10=$80-$10=$70
This means it costs $70 per month. Per year would be
$70*12=$840
400
Isolate the x variable in this equation
12y=4x-8
x=3y+2
400
Identify the slope and y-intercept of the following equation
2x+3y=12
slope: -2/3
y-intercept: 4
400
Graph the following equation AND identify the slope and y-intercept.
-4x+2y=24
The slope is 4 and the y-intercept is 12.
400
Solve the following system of equations by elimination:
{(4x-3y=22),(4x+4y=-48):}
(-2,-10)
500
London went to Pak-n-Save to get supplies for an ice cream party. She was in charge of getting ice cream and whipped cream and her budget was $40. When she got to the store, she found that a tub of ice cream cost $8 and a can of whipped cream cost $4. First, create an equation that represents how many tubs of ice cream and cans of whipped cream she can buy. Then, figure out how many cans of whipped cream London can buy if she buys 3 tubs of ice cream.
First,
40=8c+4w
Then,
c=3
40=8(3)+4w
40=24+4w
16=4w
4=w
500
Isolate the y variable
1/2x=(2y+8)/4
(2x-8)/6=y
500
Do the following two equations have the same slope OR the same y-intercept? What are the slopes and y-intercepts of both equations?
-6x+2y=-16
y=4x-8
They both have the same y-intercept of -8.
The first equation has a slope of 3 and a y-intercept of -8.
The second equation has a slope of 4 and a y-intercept of -8.
500
Graph the following two equations AND determine the coordinate at which the two equations intersect.
{(y,=,2x,+,6),(-4x,+,18,=,y):}
The two equations intersect at (2, 10).
500
Solve the following system of equations by substitution:
{(2x=3y+5),(2x+4y=19):}
(5.5,2)