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9 Extended: Working with the Slope

Complete the questions below before our next class.

  1. A line contains the point A(1, 3) and has a slope of 3. Find the coordinates of two other points on the same line.
  2. A line contains the point A(0, 5) and has a slope of \(\displaystyle{-\frac{2}{3}}\). Find the coordinates of two other points on the same line. (Hint: associate the negative sign with the number in numerator before trying to find other points on the line.)
  3. Consider the point A(1, 1). On a grid, graph a line with a slope of \(\displaystyle{\frac{3}{5}}\) that passes through point A, and a line with a slope of \(\displaystyle{-\frac{5}{3}}\) that also passes through point A. What do you notice about the two lines?

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11 SL Combinations of Transformations

For homework before next class, answer the following question.

Does the order in which we apply transformations matter? For example, if I begin with the graph of \(y=f(x)\), and I

  • (A) translate by 2 units to the left, and then
  • (B) stretch vertically by a factor of 3,

will I always get the same result as I would if I had begun with the graph of \(y=f(x)\), and I

  • (B) stretch vertically by a factor of 3, and then
  • (A) translate by 2 units to the left?

What if, instead of stretching vertically by a factor of 3, I stretch horizontally by a factor of 3? Does order matter in that case?

Consideration of the function \(f(x)=x^3-2x^2\) may help here.

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11 SL Transformations

We’ve now covered two types of transformations

  • (vertical and horizontal) translations, and
  • (vertical and horizontal) stretches.

Complete the following questions before our next class.

Exercise 5B questions 1, 2, 4, 5
Exercise 5C questions 2, 4, 5, 6, 8
Exercise 5D questions 1acde, 2, 4, 5