# Graphing and Linear Equations

1. Simplify: 6x3 + 4x2 +5 -7x3 +9x2 -4x +5

2. Evaluate -3[10+4(2 raised to the power 3) -5)-7]

3. Solve for X: -4(x + 6)-3x = 10 + (2 - x)

4. Name the property illustrated: 4(3.7)= (4.3)7

5. Graph 3x + 4y = 12

6. Find the x- and y-intercepts of y = -5x-6

7. Put 3x + 2y = -3

8. Find the slope and the line through the points (2,8) and (7,3)

9. Find the slope and the y-intercept of the line 9x + 3y =81

10. On Friday, Shawn drove to the lake in 45 minutes. On Sunday he returned up in 9 less minutes and averaged 12 more miles per hour. How far is the lake from his house.

11. Find the equation of a line that has slope -1/2 and passes through the point (6,4).

12.The waiting room at Southwest Pediatrics is 10 feet longer than it is wide. During a recent remodeling, the waiting room was wallpapered. A total of 84 feet of wallpaper border was used in the project. What are the dimensions of the waiting room?

13. Town Bank's 7% rate means Sue must spend $6.66 per $1000 of her mortgage each month, and Big Bank's 6.5% rate means she will spend $6,32 per $1000 each month. Big Bank also charges 4 points while Town Bank charges none. Sue needs an $80,000 mortgage. How long will it take for both mortgages to be equal?

14. How many pounds of gourmet candy selling for $2.80 per pound should be mixed with 2 pounds of gourmet candy selling for $1.80 a pound to obtain a mixture selling for $2.60 per pound?

15. A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus traveling at 50 miles per hour leaves for the same town and arrives at the same time as the train. If both the train and the bus traveled in a straight line, how far is the town from where they started ?

#### Solution Preview

Mathematics

1. Simplify: 6x3 + 4x2 +5 -7x3 +9x2 -4x +5

Here, you need to combine like terms (i.e. you can combine 6x^3 and -7x^3 to get -x^3, but you can't combine 4x^2 and -4x because one has an x^2 term and the other just has an x).

6x^3 + 4x^2 + 5 - 7x^3 + 9x^2 - 4x + 5

-x^3 + 13x^2 - 4x + 10

2. Evaluate -3[10+4(2 raised to the power 3) -5)-7]

Start from the innermost parentheses, and work out. There isn't a matching "(" to go with the ")" after the 5, so I took it out.

3[10+ 4(2^3) - 5 - 7]

3[10+ 4(8) - 5 - 7]

3[10+ 32 - 5 - 7]

3[42 - 5 - 7]

3[37 - 7]

3[30]

90

3. Solve for X: -4(x + 6)-3x = 10 + (2 - x)

-4(x + 6) - 3x = 10 + (2 - x)

multiply out the -4: -4x + -24 - 3x = 10 + 2 - x

combine like terms: -7x - 24 = 12 - x

add x to both sides: -6x - 24 = 12

add 24 to both sides: -6x = 36

divide both sides by -6: x = -6

4. Name the property illustrated: 4(3.7)= (4.3)7

I assume that the dots mean multiplication. The property illustrated is the associative property. This means that when you multiply (or add), it doesn't matter which terms you combine first (either the 3 and the 7 or the 4 and the 3), you will get the same answer in the end.

5. Graph 3x + 4y = 12

Solve for y:

3x - 4y = 12

-4y = -3x + 12

y = (3/4)x - 3

The y-intercept is at (0, -3) and the slope of the line is ¾.

6. Find the x- and y-intercepts of y = -5x-6

Find the y-intercept by setting x equal to 0.

y = -(0) - 6

y = -6

The y-intercept is (0, -6).

Find the x-intercept by setting y equal to 0.

0 = -5x - 6

6 = -5x

-6/5 = x

The x-intercept is (-6/5, ...