Definitions
Draw it!
Slope
Word problems
What's your name?
100
the x coordinate of the point where the graph intersects the x axis
What is the x intercept
100
Draw a function with a changing slope
Answers vary, but any nonlinear function should be fine.
100
What is the slope of a line going through (1,3) and (5,-6)?
What is -9/4?
100
If Ms. Doyle lives a certain distance d from school, and takes a certain time t to get to school on time, plot the graph showing her position as she goes to school in the morning. What does the slope represent?
See board.
100
A graph that's V - shaped: is it a function? If so, is it linear?
What is a non-linear function: passes the vertical line test, cannot be written as y = mx+b (the graph isn't a straight line).
200
all allowed x values
What is "domain"
200
Draw a linear function with a negative slope.
A line that goes down as it moves right.
200
What is the slope of the line whose x-intercept is -4 and y-intercept is 5?
What is 5/4?
200
You get paid $20 per hour for tutoring. Plot a few points corresponding to time worked (x axis) and money earned. Do they fall on a straight line?
See board.
200
A graph that is two diagonal lines crossing: a) is it a function? Explain. b) if it is, is it a linear function? Explain.
What is a non-function: fails the vertical line test.
300
all functions are this, but not all of these are functions
What is "relation"?
300
Is the parabola on its side a function or not? Explain.
No, by the vertical line test: for many inputs, there are two outputs.
300
What are x and y intercepts of the line given by y = 2x+3?
What is x-int: -1.5, y-int:3?
300
This summer you get a job as a waiter/waitress and get paid $1000 per month plus $30/hour for every hour you work on top of 80 hours per month. How many hours per week should you work assuming you want to earn $3,000 per month? (Assume you only work 4 weeks per month.)
What is 37 hours per week?
300
A graph that looks like a wave -- is it a function? If so, is it linear? Explain.
What is a non-linear function. It passes the vertical line test, so it is a function, but the graph isn't a straight line -- not a linear function.
400
a type of function that does not make a straight line when graphed
What is a "nonlinear function"?
400
Draw a relation with an undefined slope.
What is a vertical line.
400
A line through which of these points would result in the smallest slope? (2,3), (6,7), (1, 0)?
What is (1,0) and (2,3)?
400
Young children grow very fast. During the first year, they grow at 2 cm/month! If humans kept growing like this, how tall would they be at age 18? A typical newborn is 50 cm long. Graph the function and find its x and y intercepts, if any.
Graph: see board. What is y = .50+0.02*18*24 = 9.14 m!!! The x - intercept doesn't exist in this situation, and the y-intercept is 50 cm -- typical birth height.
400
George thinks that a graph that looks like a circle is a non-linear function graph. Is George right? Explain why or why not.
What is not a function -- fails the vertical line test, so George is wrong.
500
the difference in y values over the difference in x values
What is "slope"?
500
Draw a function with a slope equal to zero. Explain why the slope is 0.
What is a horizontal line.
500
You are going on a field trip to a fair. If we plot your distance from school (in miles) versus time (in hours), what does the slope of this function represent?
What is speed in miles per hour?
500
DAILY DOUBLE An amusement park charges $15 for admission and $3 per ride. Graph the price of going to the park (y axis) as a function of the number of rides you take (x axis). What do the x and y intercepts (if any) mean here?
See board. x - int: does not exist, since even taking no rides cost something. y - int: $15, how much to get into the park but not take a ride.
500
Joanna can't remember whether it's vertical ( | ) or horizontal (___) lines that have undefined slope. Explain to Joanna which is it, and why.
What is vertical lines. The slope is undefined because, for any pair of points we choose, the change in y is defined, but the change in x is 0, so we are dividing by 0 to get the slope, and we get an undefined answer.
M
e
n
u