Thread: Math help, test tommorow.

I have an test tommorow and i'm trying to do my best on it because i'm not doing too good in the class and we haven't been gaven text books yet so I can't look back in the book to figure out how to do this work, It's only work sheets,If anyone could show me an easy way to do these type of problems it'd be really apperciated, thanks

Consider the rule y=5x+7
a. How many tiles are in figure 0?
b. Which figure has 37 tiles?
c.In the equation y=mx+b what do letters m and b represent?


For each pair of lines bellow, solve the system by graphing and solve it algebracially using the Equal Values Method. Explain how the graph confirms the algebraic result
a. y=7x-5 and 7=-2x+13
b. y=3x-1 and y=3x+2

Copy and complete the table for the linear pattern bellow.
in(x) -4,-3,-2,-1,0,1,2,3,4
out(y) _, _,,_,_,_,-2,3,8,_,_

A.What is the y interpect? What is the growth factor
B.Find the rule for this line.
C.If the output number (y) is -52, what was the inut number (x)?

Originally Posted by Haxcake

Consider the rule y=5x+7
a. How many tiles are in figure 0?
b. Which figure has 37 tiles?
c.In the equation y=mx+b what do letters m and b represent?

a) Not sure what that means. If you mean what is 'y' when x=0 then it is,
y=5(0)+7=7

b)Again I assume the same. You want to know for what 'x' do you get an output value of 37. Simple,
37=5x+7
How do you solve?
Subtract 7 from both sides,
30=5x
Now divide both sides by 5,
x=6.
All you need to do now is check, and it does work!

c) m represent the slope of the line. That is how steep it is. When the slope if big the line is getting closer and closer to a vertical line. When the slope is small, m=0 then it is a horizontal line. The 'b' terms shows the y-intercept that is the point on the y axis where the line crosses it. That means to find an equation of a line you need a slope and an intercept.

Originally Posted by Haxcake

For each pair of lines bellow, solve the system by graphing and solve it algebracially using the Equal Values Method. Explain how the graph confirms the algebraic result
a. y=7x-5 and 7=-2x+13

Set them equal to each other,
7x-5=-2x+13
Add 2x to both sides thus removing -2x on left side,
9x-5=13
Add 5 to both sides,
9x=18
Divide by 9,
x=2
Substitute that value into any equation you want, say #1,
y=7(2)-5=14-5=9
Thus they intersect at,
(x,y)=(2,9)

b. y=3x-1 and y=3x+2

A tricky one, when you set them equal,
3x-1=3x+2
Note the left hand side is always larger then right hand thus they cannot be equal.
Alternatively assume that,
3x-1=3x+2
Subtract 3x from both sides,
-1=2
Which is not true, meaning our assumption was wrong, that is there are no solutions. Graphically it means both lines are parallel. See below.

Originally Posted by Haxcake

Copy and complete the table for the linear pattern bellow.
in(x) -4,-3,-2,-1,0,1,2,3,4
out(y) _, _,,_,_,_,-2,3,8,_,_

A.What is the y interpect? What is the growth factor
B.Find the rule for this line.
C.If the output number (y) is -52, what was the inut number (x)?

I assume, for the table, you have one extra _, since you have 9 values for x and 10 for y. I think you mean:

When x = 0, y = -2
When x = 1, y = 3
When x = 2, y = 8

Just by that information, you can tell that the y intercept is -2.
Try plotting some points on a graph.

(0,-2)
(1,3)
(2,8)...

What is the slope ["growth factor"]? Each time, you go UP 5, and OVER 1.

Definition of slope: rise / run (Rise over run).

So, in this case, the rise is 5, and the run is 1. 5/1 = 5.

Or, slope in general is given by the formula:

[(y_2 - y_1) / (x_2 - x_1)]

Take any two points and do that:

Lets take (1,3) and (2,8):

[(8 - 3) / (2 - 1)] = [5/1] = 5.

Therefore, the general equation is:

y = mx + b

y = 5x - 2 (b is the y-intersect). [this is for part b].

Completing the table is simple now:

in(x) = -4,-3,-2,-1,0,1,2,3,4
out(y) = -22,-17,-12,-7,-2,3,8,13,18

Do you see that y keeps increasing by 5 (IE: the slope)?

For part c, if y = -52, what was the input, x?

Plug it in!

-52 = 5*x - 2. Solve for x.

-50 = 5*x

Divide both sides by 5.

-10 = x