1.12 Lines

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 $n$ ? 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.

Your parachute opens when you are 2,000 feet above the ground. (Call this time $t=0$ .) 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 $t$ 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.

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.

Compute the slope of a line that goes from $(\mathrm{1,3})$ to $(\mathrm{6,}\text{18})$ .

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

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.

$y=\mathrm{3x}-2$

Slope:___________

$y$ -intercept:___________

Other point:___________

$\mathrm{2y}-x=4$

Equation in $y=\text{mx}+b$

Slope:___________

$n$ -intercept:___________

Other point:___________