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Function Homework -- Lines

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems designed to develop some concepts related lines and graphing.

Exercise 1

You have $150 at the beginning of the year. (Call that day “0”.) Every day you make$3.

• a. How much money do you have on day 1?
• b. How much money do you have on day 4?
• c. How much money do you have on day 10?
• d. How much money do you have on day n n? This gives you a general function for how much money you have on any given day.
• e. How much is that function going up every day? This is the slope of the line.
• f. Graph the line.

Exercise 2

Your parachute opens when you are 2,000 feet above the ground. (Call this time t=0t=0 size 12{t=0} {}.) Thereafter, you fall 30 feet every second. (Note: I don’t know anything about skydiving, so these numbers are probably not realistic!)

• a. How high are you after one second?
• b. How high are you after ten seconds?
• c. How high are you after fifty seconds?
• d. How high are you after t t seconds? This gives you a general formula for your height.
• e. How long does it take you to hit the ground?
• f. How much altitude are you gaining every second? This is the slope of the line. Because you are falling, you are actually gaining negative altitude, so the slope is negative.
• g. Graph the line.

Exercise 3

Make up a word problem like exercises #1 and #2. Be very clear about the independent and dependent variables, as always. Make sure the relationship between them is linear! Give the general equation and the slope of the line.

Exercise 4

Compute the slope of a line that goes from (1,3)(1,3) size 12{ $$1,3$$ } {} to (6,18)(6,18) size 12{ $$6,"18"$$ } {}.

Exercise 5

For each of the following diagrams, indicate roughly what the slope is.

Exercise 6

Now, for each of the following graphs, draw a line with roughly the slope indicated. For instance, on the first little graph, draw a line with slope 2.

For problems 7 and 8,

• Solve for y y, and put the equation in the form y=mx+by=mx+b size 12{y= ital "mx"+b} {} (…if it isn’t already in that form)
• Identify the slope
• Identify the y y-intercept, and graph it
• Use the slope to find one point other than the y y-intercept on the line
• Graph the line

Exercise 7

y=3x2y=3x2 size 12{y=3x - 2} {}

Slope:___________

y y-intercept:___________

Other point:___________

Exercise 8

2y x = 4 2y x = 4 size 12{2y - x=4} {}

Equation in y=mx+by=mx+b size 12{y= ital "mx"+b} {}

Slope:___________

n n-intercept:___________

Other point:___________

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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