Week 1: Lines – Day 5

True or False?

1. The graph of a straight line in the x-y plane can have a y-intercept or an x-intercept, but not both.

2. If F(x) = 2x + 1, then:

F(z) + F(w) = F(z + w)

3. If G(x) = 3x, then:

G(z) + G(w) = G(z + w)

4. It is impossible for a line with slope 10 to pass through the point (5, 5).

5. If two lines in the x-y plane have two points in common, they have all points in common.

Week 1: Lines – Day 4

1. An alien space baby is born on Year Zero. At birth, the baby is 10 cm tall. The baby grows 1 cm taller per month, or 12 cm per year. If x is the time in years after Year Zero, write an equation that describes the height of the baby as a function of the year.

2. How tall is the alien space baby of problem 1 at the age of 5 years?

3. How tall is the alien space baby of problem 1 at the age of 30 years?

Bonus question: if the alien space baby looks human, when would people start to suspect that the alien space baby is an alien?

4. Betty’s sequoia tree grows one ring per year. Let x be the current year (2014). Betty takes a core sample and finds out that her tree has 157 rings in the year 2014. Write an equation that describes the number of rings in the sequoia tree as a function of the calendar year x.

Bonus: what year was the sequoia tree born?

5. The equation for the number of rings in Betty’s sequoia tree as a function of calendar year, when you graph it, is the equation of a straight line. Does Betty’s sequoia tree grow in a manner similar to the alien space baby? Why or why not?

Some things to think about: how does a typical human grow? What would your own human height as a function of age look like, compared to the alien space baby’s? What are some different ways to measure the growth of a tree? What if, instead of rings, you measured the tree’s gain in diameter each year – what kind of function would that be?

Week 1: Lines – Day 3

1. Is the point (0, 0) on, above, or below the line y = 3x + 2?

2. Is the point (-1, 5) on, above, or below the line x + y = 4?

3. Do the lines y = 17x – 1 and y = 15x – 1 intersect?

4. Are the points (2, 3), (-5, 10) and (0, 5) collinear? (Collinear means they all lie on the same line.)

5. Are the points (1, 4), (2, 8), and (3, 13) collinear?

Week 1: Lines – Day 2

1. What is the equation of the line through the points (0, 0) and (4, 3)?

2. What is the equation of the line through (0, 5) and (-1, 7)?

3. What is the equation of the line through (3, 3) and (6, 3)?

4. What is the equation of the line that has a slope of 4 and a y-intercept of (0, 10)?

5. What is the equation of the line through (7, 5) and (7, 10)?

Week 1: Lines – Day 1

1. What is the slope of the line:

y = 2x – 5

2. Which line is steeper:

x – 3y =4
or
3x – y = 2

3. What is the slope of a line parallel to:

y = (7x + 14)/2

4. Write down an equation of a line parallel to:

y = 3 – 5x

5. Is the point (2, 10) on, above, or below the line  y – 4x  =  2 ?