Algebra 2Name: ______

Slope, lines, and graphs! Oh my!Date: ______

Consider the line graphed here:

  1. What is the slope?
  1. What is the y-intercept?
  1. What is the equation (function)?
  1. Find three points on this line:
  1. Where does the line cross the x-axis?

y-intercept:

x-intercept:

Now, consider this function: f(x) = 4x – 12

  1. What is the y-intercept of the line?
  1. What is the x-intercept of the line?
  1. What is the rate of change?
  1. Find three points on this line:

Consider this equation: 4x + 3y = 12

  1. What is the y-intercept of the line?
  1. What is the x-intercept of the line?
  1. What is the slope of the line?
  1. What is the equation of the line in y = mx + b form?
  1. Find three points on this line:

If a line goes through (0, -4) and (2, 0) find the following:

  1. What is the slope of the line?
  1. What is the equation of the line in slope-intercept form?
  1. What is the y-intercept?
  1. What is the x-intercept?
  1. Find three (other!) points on this line:

HORIZONTAL & VERTICAL LINES

Write the coordinates of each point:

A: ______B: ______A: ______B: ______

C: ______D: ______C: ______D: ______

Write the equation of each line:

______

Practice: Find the slope and the equation of each line:

1. m = ______2. m = ______3. m = ______

eqn: ______eqn: ______eqn: ______

4. m = ______5. m = ______6. m = ______

eqn: ______eqn: ______eqn: ______

RECAP:

  1. The slope of a horizontal line is always ______.
  2. The slope of a vertical line is always ______.
  3. A vertical line does not cross the ____ - axis.
  4. The equation of a horizontal line is ______.
  5. The equation of a vertical line is ______.

Slopes of Parallel and Perpendicular Lines:

Parallel Lines:Perpendicular Lines:

Tell whether the lines are parallel, perpendicular, or neither.

1. line 1: (-2, 2) and (0, -1)2. line 1: (1, 2) and (4, -3)

line 2: (-4, -1) and (2, 3) line 2: (-4, 3) and (-1, -2)

Write the equation of the line that passes through the given point and satisfies the given condition.

  1. (-3, -5); parallel to y = 4x + 12. (7, 10) ; parallel to y = -x + 3

3. (2, 8); perpendicular to y = -3x +2 4. (4, 1) ; perpendicular to y = ½ x - 2

Problem Solving!

5. You buy a used car for $6500. The monthly cost of owning the car (including insurance, fuel, maintenance, and taxes) averages $350.

a. Write an equation that models the total cost of buying and owning the car. (f(x) = total cost, x = # months)

b. How much have you spent on the car after 6 months?

6. Rate of Change:

You decide to join a gym. They are having a special sale on membership! The Get Big Quick gym has a $5 membership fee and only costs $2 per month.

Fill in the chart modeling the situation:

# of Months / 0 / 1 / 2 / 3 / 4 / 5 / 6
Total Cost

a. Write a function for this situation:

b. How much would 13 months cost at this gym?

c. If you have spent $47, how long have you been a

member of this gym?

d. What is the y-intercept of this line?

e. What is the x-intercept of this line?

Find the average rate of change. Be sure to include units.

7. In 1998, Linda purchased a house for $144,000. In 2009, the house is worth $245,000. Find the average annual rate of change.

8. Kevin's savings account balance changed from $1140 in January to $1450 in April. Find the average rate of change per month.