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# Equations of lines

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Answer problems on attached word document.

If possible show work. I have a lot more questions to answer and I need to use examples to work through them.

1. Find the slope for 3y - 1 = 14

2. Find the equation of the line in the form y = mx + b if possible if the line goes through (2, -3) and (-3, 4).

3. Find the equation of the line in the form y = mx + b if possible if the line goes through (0, 5) and it is perpendicular to
8x + 5y = 3

4. Graph: 3x - 5y = 15

5. Graph: x + 2 = 0

6. Supply: For a new diet pill, 60 pills will be supplied at a price of \$40, while 100 pills will be supplied at a price of \$60. Write a linear supply function for this product.

7. Find the equilibrium price and quantity for the diet pills in exercises 34 and 35. The answer to #35 is

8. Break-Even Analysis. The cost function for flavored coffee at an upscale coffeehouse is given in dollars by C(x) = 3x + 160, where x is in pounds. The coffee sells for \$7 per pound.
a. Find the break-even quantity.

b. What will the revenue be at that point?

9. The average new car cost for the years from 1975 to 2000 is given in the table where x is the number of years since 1900?
Year (x) 75 80 85 90 95 00
Cost (y) 6000 7500 12,000 16,000 20,400 24,900

a. Find an equation for the least squares line.
b. Use your equation from part a to predict the average cost of a new car in the year 2005. (x = 105)
c. Find and interpret the coefficient of correlation. Does it indicate that the line is a good fit for the data?
d. Plot the data. Does the scatterplot suggest the trend might not be linear?

10. Find the size of each matrix, find the values of any variables, and identify any square, row, or column matrices.

11. Find 3C + 2A if it exists. Be sure to show any intermediate steps.

12. Find AC if it exists. Be sure to show any intermediate steps.

13. Find ED if it exists. Be sure to show any intermediate steps.

14. Find the inverse of each matrix if it exists.

15. The following system of equations is given.

a. Solve by the echelon method.
b. Solve by the Gauss-Jordan method.
c. Write the system as a matrix equation AX = B
d. Find the inverse matrix A from part C.
e. Solve the system using A-1 from part d.

16. Find the equation of the line in the form y = mx + b if possible if the line goes through (5, -2) and (1,3)