Slope
Slope-Intercept Form
Scatter Plots/Correlation and Causation
Parallel Lines
Perpendicular Lines
Inverses of Linear Functions
100
What is the formula to find the slope?
What is m= y2-y1
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x2-x1
100
Write an equation in slope-intercept form of the line with the slope m=-4 and y-intercept b = 5.
What is y=-4x+5
100
Tell the three types of relationships that can be shown in a scatter plot.
What is positive, negative, and no relationship?
100
Parallel Lines have what kind of slopes?
What is the same slope?
100
Perpendicular Lines have what kind of slope?
What is opposite reciprocal?
100
What is the inverse of f(x)?
f-1(x)
200
A slope equal to 0 is what kind of line?
What is horizontal?
200
Write an equation of the line in slope-intercept form of the line have the slope m=1 and passing through the point (2,5).
What is y = x + 3?
200
As x increases, y decreases. What kind of relationship would this display?
What is a negative relationship?
200
Determine whether the graphs of the equations are parallel: 2y=4x+8 and y=2x-7
If they are parallel, explain why
Yes they are parallel - same slope
200
Determine whether the graphs of the equations are perpendicular:
y=1/5x + 2
-3y + 3x = -15
No - the slopes are flipped but not changed signs.
200
Find the inverse of the set f(x) = {(-3, 6)(7, -2)(5, 1)} using the correct format.
f-1(x) = {(6,-3)(-2,7)(1,5)}
300
Determine the slope of the line passing through the points (7,6) and (0,2)
What is 4/7?
300
Write an equation in slope-intercept form of the line passing through the points (-4,4) and (2,1).
What is y = -1/2x + 2?
300
Determine whether the graphs of the equations are parallel, perpendicular or neither: y = -3/4x - 2 and 3y= 4x +12 and 2y - 3x = 10
The first and second lines are perpendicular but the 3rd isn't anything.
300
Write an equation in slope-intercept form of the line that is parallel to the graph y=-4x+8 and passes through (1,3).
What is y=-4x+7
300
Write an equation in slope-intercept form of the line that is perpendicular to the graph y=1/3x - 2 and passes through (-4,2).
What is y = -3x - 10?
300
Graph the points {(-2, -3)(-1,0)(0,3)}.
Now graph the inverse of that line.
400
An undefined slope is what kind of line?
What is vertical?
400
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5 feet away. After 2 seconds, the car is 35 feet away. Write a linear equation in slope-intercept form to find the distance of the car from Greg.
y = 15x + 5
400
Isabel owns a small hair salon. She discovered a positive correlation between the number of clients she has and the amount of money she makes each week. Does this situation show causation? Explain your answer.
Yes - the number of clients causes Isabel to make money
400
Write an equation in slope-intercept form of the line that is parallel to the graph 3x+2y=9 and passes through (2,0).
What is y=-3/2x + 3
400
Write an equation in slope-intercept form of the line that is perpendicular to the graph 2x + 3y = 2 and passes through (3,0).
What is y = 3/2x - 9/2?
400
Find the inverse of the function g(x) = -16 - 4/3x
g-1(x) = -3/4x - 12
500
Find the slope of the line passing through the points (-2,-3) and (-5, -3).
What is -3/0 or undefined.
500
An online magazine allows you to view up to 25 articles for free. To view 30 articles, you pay $49.15. To view 33 articles, you pay $57.40. Write a linear equation in the form y = mx + b for the cost of the online magazine if you view 30 or more articles.
y = 2.75x + 35.40
500
Jane compared places to eat in her town and found that the more fast food places there were, the less upscale restaurants there were. Determine if there is correlation but not causation or causation between the fast food and upscale restaurants.
Correlation but not causation
Increased fast food restaurants does not cause there to be less upscale restaurants
500
Scientists excavating a dinosaur mapped the site on a coordinate plane. If one bone lies from (-5,8) to (10,-1) and a second bone lies from (-10,-3) to (-5,-6), are the bones parallel? Explain.
Yes, both have a slope of -3/5
500
In the ruins of an ancient civilization, an archaeologist found pottery at (2,6) and hair accessories at (4,-1). A pole is found with one end at (7,10) and the other end at (14,12). Is the pole perpendicular to the line through the pottery and hair accessories?
Yes. The slopes are -7/2 and 2/7
They are negative reciprocals of each other.
500
At the start of the mowing season Chuck collects a one-time fee of $25 from his customers. He charges the Foster family $45 for each mow. The amount collected from the Foster's this summer is C(x) = 25+45x where "x" is the number of times Chuck mowed the lawn.
a) Find the inverse function
b) What do "x" and C-1(x) represent in the inverse?
c) How many times did Chuck mow if he collected $1015 from the Fosters?
a) c-1(x) = 1/45x - 5/9
b) x is the amount of money, C-1(x) is the number of times he mowed.
c) 22 times