Help? algebra? asap? please?

~ If g(x)=-7x+2, find g(-6)

g(-6) means that your x = -6, thus, substituting it in:

g(-6) = -7(-6)+2

g(-6) = 42+2

g(-6) = 44

Answer = D

~ Determine the slope of the line that passes through the points (-4,-2) and (-1,-1)

I think this is gradient? I'm not so sure. xD

Gradient, m = [-1-(-2)]/[-1-(-4)]

..................= [-1+2]/[-1+4]

..................= 1/3

Answer = A

~ Solve the system of equations: y=2x-10 and x-y=7

y = 2x - 10 ------------------- Eq. 1

x - y = 7 ------------------------ Eq. 2

From Eq. 2:

x - y = 7

.....x = 7 + y ---------------- Eq. 3

Substitute Eq. 3 into Eq. 1:

y = 2x - 10

y = 2(7+y) - 10

y = 14 + 2y - 10

y = 4 + 2y

y - 2y = 4

-y = 4

y = -4

Substitute y = -4 into Eq. 3:

x = 7+ y

x = 7 + (-4)

x = 7 - 4

x = 3

1) Substitute.

g(-6) = -7(-6) + 2 = 42 + 2 = 44

Answer: d

2) Use the point-slope formula.

(-1+2)/(-1+4) = 1/3

Answer: a

3) Move all variables on the left side of the equation.

2x - y = 10

-x + y = -7

x = 3

y = 3 - 7 = -4

Answer: (3,-4)

First Question: g(-6) just mean substitute the x with -6. Like this -7(-6)+2 Solve and get 44

g(x) means g is a function of x

Second Question: Use rise over run

rise

-----

run

Graph and count the units going up (or down) to get to the level of the next point starting at (-4,-2). This amount is 1 unit up which means positive 1. Then count the units,going left or right, to get to the point. This number is 3 to the right which means positive 3.

It ends up like this:

rise -1

----- ----

run -3

If you do it starting at the point (-1,-1):

Graph and count the units going down (or up) to get to the level of the next point starting at (-1,-1). This amount is 1 unit down which means negative 1. Then count the units,going left or right, to get to the point. This number is 3 to the left which means negative 3.

It ends up like this:

rise -1

----- ----

run -3

*Cross out the negative since if the divide a negative number by a negative number, you get a positive number.

Answer: 1/3

This method only works for graphs with a straight line going through them. I am pretty sure they're called linear graphs.

Question three:

This type of equation you can use the method substitution.

y=2x-10

x-y=7

Y EQUALS 2x-10. Therefore you substitute 2x-10 into x-y=7 in place of y.

Like this: x-(2x-10)=7

Now you solve: x-(2x-10)=7

.......distributing: x-2x+10=7

combine-like terms: -x+10=7

..........working: ,,,,,,,,,,-10,,-10 (subtracting - 10 from both sides)

..........working: -x=-3

..........working: -x/-1=-3/-1 (diving by -1 on both sides to get rid of minus sign on the x)

Answer: x=3

Substitute x into one of the equations:

y=2(3)-10

y=6-10

y= -4

The other equation (just to make sure I'm correct)

(3)-y=7

-3.....-3

-y=4

-y/-1=4/-1

y= -4

and

x=3

replace x by -6

g(x)=-7x+2

g(-6)=-7(-6)+2 = -40 answwer b

slope =(y2 - y1) / (x2 - x1) = (-1 - (-2) ) /(-1 - (-4) ) = (-1 + 2) / (-1 + 4) = 1 / 3 answer a

y = 2x-10

x - y = 7 x = 7 + y

put into first eqaution

y = 2 (7 + y) - 10

y = 14 + 2 y - 10

y - 3y = 14 - 10 = 4

-2 y = 4

y = -2

Put into other equation to get x

Looks like homework you are too lazy to attempt!

1)D

2)A

3)x=3, y=-4

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