# Equations and graphing

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1. Rewrite the equation 4x - 10y = 11 as a function of x.

2. Write the equation of the line that passes through point (1, -8) with a slope of 0.

3. Given f(x) = 5x2 - 3x + 1, find f(-2).

4. Write the equation of the line passing through (-6, -3) and (-6, 1).

5. One day, the temperature at 9:00 A.M. was 42°F, and by 2:00 P.M. the temperature was 57°F. What was the hourly rate of temperature change?

6. Find the slope of any line perpendicular to the line through points (6, 3) and (7, 7).

7. Match the graph with one of the equations.

8. Find the slope and y-intercept.

x = -8

9. Solve the following system of linear inequalities by graphing.

x - 2y  4

x  4

10. Solve the following system of linear inequalities by graphing.

x + 2y  3

2x - 3y  6

11. Solve the system by addition or substitution.

4x - 4y = -8

y = 2 + x

12. Solve the system by substitution.

5x + 3y = -19

y = -2x - 8

13. Solve the system by addition.

-4x + 7y = -10

x - 5y = 9

14. Graph the inequality.

2x + 3y > 6

15. Write the equation of the line with x-intercept (12, 0) and y-intercept (0, 4).

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##### Solution Summary

This provides several examples of working with graphing inequalities and equations and solving systems of linear equations.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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