1. Find the y-intercept of the line represented by the following equation. -2x + 2y = 16
2. Write the equation of the line with slope -4 and y-intercept (0, -9).
3. Write the equation of the line with slope and y-intercept (0, 3).
4. One day, the temperature at 9:00 A.M. was 49°F, and by 3:00 P.M. the temperature was 61°F. What was the hourly rate of temperature change?
5. Determine which two equations represent parallel lines.
(a) y = -7x + 3 (b) y = 7x + 3 (c) y = x + 3 (d) y = -7x + 6
6. Determine which two equations represent perpendicular lines.
(a) y = x - 5 (b) y = 5x - (c) y = x + (d) y = x -
7. Are the following lines parallel, perpendicular, or neither?
L1 through (-4, -7) and (1, 3)
L2 through (2, 6) and (4, 10)
8. Are the following lines parallel, perpendicular, or neither?
L1 with equation x - 5y = 25
L2 with equation 5x + y = 5
9. Find the slope of any line perpendicular to the line through points (8, 4) and (9, 7).
10. A line passing through (6, -10) and (-1, y) is perpendicular to a line with slope . Find the value of y.
11. Use the concept of slope to determine whether the given figure is a right triangle (i.e., does the triangle contain a right angle?).
12. Write the equation of the line that passes through point (0, 9) with a slope of 6.
13. Write the equation of the line passing through (1, -8) and (1, 3). Write your results in slope-intercept form, if possible.
14. Write the equation of the line with x-intercept (-9, 0) and undefined slope. Write your results in slope-intercept form, if possible.
15. A copier was purchased by a company for $7,500. After 5 years it is estimated that the value of the copier will be $4,500. If the value in dollars V and the time the copier has been in use t are related by a linear equation, find the equation that relates V and t.
16. You have at least $60 in change in your piggy bank, consisting of quarters and pennies. Write an inequality that shows the different number of coins in your piggy bank.
17. If f(x) = -x3 - x2 + 2x + 6, find f(-2), f(0), and f(3)
18. Rewrite the equation y = 2x + 2 as a function of x.
19. The inventor of a new product believes that the cost of producing the product is given by the function: C(x) = 2.75x + 2,000. How much does it cost to produce 6,000 units of his invention?
20. Given f(x) = -5x + 3, find f(a + 1).
21. Write the equation of a line that passes through (0, 4) and has a slope of -1/5.
22. Write the equation of a horizontal line with a y-intercept of 7.
23. What is the slope and the y-intercept of y=3x+1?
24. What is the slope and y-intercept of y=-3?
25. What is the slope and y-intercept of 6x+y=10?
26. Determine whether the lines are parallel, perpendicular, or neither.
Y=-3x+1
Y=-3x-8
27. Determine whether the lines are parallel, perpendicular, or neither.
2x-y=-10
2x+4y=2
28. Determine whether the lines are parallel, perpendicular, or neither.
Line 1 passes through (0, 3) and (2, 5)
Line 2 passes through (5, -4) and (-3, 3)
29. Write the equation of a line that passes through (4, 0) and (-4, -5). Write your answer in slope-intercept form.
30. Write the equation of a line that passes through (-1, 2) and (3, 5). Write your answer in slope-intercept form.
31. Write the equation of a line that passes through (1, -45) with a slope of -3. Write your answer in slope-intercept form.
32. Write the equation of a line that passes through (-2, 5) with a slope of -4. Write your answer in slope-intercept form.
33. Write the equation of a line that passes through (-2, 5) and (-6, 13). Write your answer in slope-intercept form.
34. f(x)=1/2x Find f(0)
35. f(x) = 4x^2+3x Find f(-2)
36. f(x)=3x+3 Find f(-1)
37. f(x)=5x^2-7 Find f(0)