Number of Solutions
How do we know when an equation has no solution? What format will it be in and what does it mean?
a=b
Variables cancel out and it is a number equal to a different number
TRIPLE POINT QUESTION: Write an equation of a line that has a slope of 5 and a y-intercept of 2
y=5x+2
Which function has a greater rate of change?
Function A: -3/2
Function B: 2/3
Function A.
If our line is going up we know its has what kind of association? And what does it tell us about our slope?
Positive linear relationship. Our slope will be positive.
DOUBLE POINT QUESTION: What is our formula to find the slope?
change in y/change in x.
How many solutions does the follow equation have?
6x + 10 = 2(5x+2)-3
One solution
Write an equation for a line that has a slope of 2 and passes through the point (4, - 3).
y=2x+11
DOUBLE POINT QUESTION: Which function has a greater ROC?
Function A: y=-.75X+10
Function B: y=-1x+10
Function B.
TRIPLE POINT QUESTION: How do we know our line of best is accurate?
Relatively equal amount of data points on each side of our line and it follows the trend
What type of relationship exists when it goes through the origin?
Proportional.
How many solutions does the following equation have:
4x-2=2(2x+3)-8
Infinite
Write an equation for a line that goes through the points (0,9) and (3, 12).
y=x+9
Car 1 traveled at 65 miles her hour but got a head start of 30 miles. Car 2 traveled 70 miles per hour but did not get a head start. Who is traveling at a greater rate?
Car 2.
When forming an equation for a line of best fit, what should you look at first?
The y-intercept/where the line crosses the y-axis.
A relationship exists between the age of a person and how much their life insurance costs. In this relationship, what is the independent variable and what is the dependent variable?
IV: Age
DV: Cost of insurance
Find a value for j and k that makes this equation have only one value for x that makes the equation true.
3(2x+5) = jx + k
j = any number but 6
k = any number but 15
Write an equation for a line that goes through the points (-3,-5) and (2, 10).
y=3x+4
Student A studied for 3 hours and got a 75 percent on their IA1. Then studied 6 hours and got a 85 on their IA2.
Student B studied 2 hours for their IA 1 and got an 75 and then studied for 6 hours and got a 85 on their IA2.
Who had a greater Rate of Change? What was their ROC?
Student A. 10/3 or 3.33.
The graph trends down and is decreasing.
The independent variable substitutes in for ____, and the dependent variable substitutes in for ___.
IV --> x.
DV --> y.
Find a value for j and k that makes the following equation have infinite number of solutions.
4(5x+7) = jx + k
j=20
k=28
Write an equation from the table.
x: 1 2 3 4
y: 5 7 9 11
y=2x+3
Lawn mower A cut 4 lawns in 5 hours and 6 lawns in 8 hours. Lawn mower 2 cut 2 lawns in 2 hours and 4 lawns in 5 hours. Who mows at a faster rate? Explain what the fastest mowers ROC means in the context of this problem.
Lawn Mower A. They mowed 3/2 of a lawn every hour.
1. Get two points from our line of best fit
2. Find the slope
3. Find the y-intercept
4. Create the equation
Subtracting a negative is the same as ______.
Adding a positive.