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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.

Figure 1: a.
A graph of a line with a steep negative slope.
Figure 2: b.
A graph of a line with a slight positive slope.
Figure 3: c.
A graph of a line with a steep positive slope.
Figure 4: d.
 (lines5d.png)
Figure 5: e.
A graph of a line with a zero slope.
Figure 6: f.
A graph of a line with a negative slope.

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.

Figure 7: b. Draw a line with slope m = 1 2 m = 1 2 size 12{m= { { - 1} over {2} } } {}
A blank graph.
Figure 8: b. Draw a line with slope m = 1 2 m = 1 2 size 12{m= { { - 1} over {2} } } {}
A blank graph.
Figure 9: c. Draw a line with slope m = 1 m = 1 alignl { stack { size 12{m=1} {} # {} } } {}
 (lines6c.png)

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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