Types of Equations
Is it a Solution?
Vocabulary
Word Problems
Substitution
100
In the form y=mx+b, what does our m tell us, and what does our b tell us?
*list both answers for points*
m=slope
b=y-intercept
100
What is the solution to this system of equations?
(-2,1)
100
What is this form of linear equation called?
Ax+By=C
Standard form
100
What does the variable x represent in this scenario?
Mark gets a new job and receives a signing bonus of $2,000. Every month he gets paid $5,000
y=total amount Mark received from his new job, x=?
x=the number of weeks Mark has worked at his job.
100
Solve for y
3x-5y=10
y=(3/5)x-2
200
What is the slope of the line y=-2x-12
m=-2
200
Why are there no solutions to this system of equations?
The lines are parallel, the slopes are the same, the lines will never intersect
200
When looking at the graph of a system of equations with two lines, where can we find the solution?
The point where the lines intersect.
200
You have two trees in your backyard. Before an upcoming storm you apple tree has 215 apples on it, and your lemon tree has 175 lemons. The wind is so strong that every hour 4 apples fall off of. the apple tree. The lemon branches are quite stronger, so only 2 apples fall from the tree each hour.
If you were to write an equation to represent the amount of fruit in each tree since the beginning of the storm, what would be the slope of each equation?
Apple tree slope: m=-4
Lemon tree slope:m=-2
200
Solve the following system of equations using substitution
y=4, y=-2x+10
*give the coordinate point of the solution
(2,4)
300
What is the equation of this line?
*write your answer in slope intercept form*
y=(3/4)x-5
300
Is (4,-4) a solution to the following system of equations?
4x+y=2, y=x-8
No, it is only a solution to one of our lines.
300
What kind of lines in a system of equations give us zero solutions?
Parallel lines
300
Write an equation in slope intercept form that describes the following scenario.
Student B's grade is a 42. Every missing assignment she turns in brings up her grade 3 percent.
y=student B's grade in this class
x=number of missing assignments Student B turns in
y=3x+42
300
Solve for x:
3(x-6)=12x-9
x=-1
400
What is the x intercept of the line 21x-32y=42?
*give the full coordinate point*
(2,0)
400
Graph the following lines to determine the number of solutions:
y=-2x+5, 4x+27=10
Infinite Solutions
400
What are lines that intersect at a 90 degree angle called?
Perpendicular lines
400
You are racing your little sibling to see who can run to a tree 100 yards away the fastest. Since your sibling is younger, you agree that they can have a 15 yard head start. You can run 6.5 yards in one second and your sibling can run 5 yards per second. Who won the race?
You won! It took you about 15.4 second to reach 100 yards and it took your sibling 17 seconds
400
Solve using substitution
2x-3y=-1, y=x-1
*give the coordinate point of the solution
(4,3)
500
Convert the following equation to slope intercept form:
8x+2y=6
y=-4x+3
500
Solve for the solution to this system of equations
y=2x+5, 3x-4y=10
(-6,-7)
500
What is the initial value of the following scenario?
You open a savings account and immediately deposit $25 into it. Each week you take $15 out of your paycheck and add it to this account.
$25, (0,25)
500
A leaky water tank originally held 80 gallons of water. Because the tank was not properly sealed, 5 gallons of water leak out every hour. Right as the tank starts leaking, you begin filling up an empty water cooler at the rate of 15 gallons per hour. How many hours will it take for both containers to have the same amount of water in them? How many gallons of water will each container have?
After 4 hours both containers will have 60 gallons of water.
500
Solve using substitution
−5x + y = −2, −3x + 6y = −12
*give the coordinate point of the solution
(0,-2)