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.
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?
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?
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)?
1. What is the slope of the line:
y = 2x – 5
2. Which line is steeper:
x – 3y =4
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 ?