Exam 1 Review

MAT 135

Closed Book-No notes. The only permitted electronic device is a non-graphing calculator.

For exam 1 you should be able to:

  1. Use function notation. ex. If f(x) = -3x+4 find f (-5)
  2. Graph linear equations
  3. Work with horizontal and vertical lines
  4. Calculate the slope of a line.

5 Determine the equation of a line given two points or one point and the slope

7. Given the equation of a line, find the slope and y-intercept

8. Do word problems involving linear equations

9. Find the slope and y-intercept of the regression line (best fitting line)

Practice problems.

1. Let f (x) = 8 – 5x. Find:

a. f (5 ) = b. f ( -3 ) =

  1. Find the equation of the line that goes through the point (-6, 3) with slope -2.
  1. What is the slope and y intercept of the line x = 2y – 18?

The slope is ______. The y intercept is ______.

  1. Consider the line 3x + 2y = 12.
  1. The x intercept is ______.
  1. The y intercept is ______.
  1. Graph the line.
  1. Find the equation of the line through (-2, 8) and (1, -7).
  1. Find the equation of the line with x-intercept 4 and y-intercept -8.

7. The slope of a horizontal line is ______. The slop of a vertical line is ______.

8. Graph the lines

(a.) x = -2(b.) y = 4.

9.Find the equation of the line passing through (1,2) that is parallel to the line with equation 3x-6y=8.

10.Find the equation of the line passing through (-1,3) that is perpendicular to the line with equation y=(2/3)x-9.

11. The sales of a small company were $20,000 in its second year of operation and $ 80,000 in its sixth year. Let y represent sales in the x-th year of operation.

  1. Use the given information to find an equation of the sales line in slope-intercept form.
  1. What are the sales in the ninth year?
  1. Find the linear cost function if 20 units cost $1800 and 70 units cost $2300.

C(x) = ______x + ______

  1. The table below shows the results of an experiment in which weights of various sizes were loaded on the end of a length of piano wire. The first column shows the weight of the load. The second column shows the measured length. Calculate the linear regression line.

Weight (x) / Length (y)
0 kg / 439.00 cm
2 / 439.12
4 / 439.21
6 / 439.31
8 / 439.40
10 / 439.50
  1. Suppose the total cost, C (x), of producing x units is given by C(x) = 4x + 550. Find:
  1. Total cost of 200 units.
  1. Fixed cost.
  1. Variable cost per unit.
  1. If the selling price per unit is $15, write the revenue function
  1. Find the break-even number of units.
  1. What revenue is received if that number of units is sold? (Use your answer to part e.)
  1. Write the specific simplified profit function for this information. Completely simplify.
  1. Find the profit on 100 units.
  1. How many units should be sold to make a profit of $1000?