Algebra 1 help, please?

Question

Literal equations? I just learned this today, and it was taught very briefly so I'm getting unsure here and there.

Write the equation in fuction form:
8x + y - 4 = 0

4x + 2y = 14

4y - 4x +4 = 0

I just need help and some explaining. I really appreciate it.

Answer 1

Solve the equation for y (i.e. rewrite so it is in the form y=) and then replace y with f(x).

8x+y-4=0 becomes y = -8x + 4 so in function notation f(x) = -8x+4

4x + 2y = 14 becomes y = -2x + 7 so f(x)=-2x+7

4y-4x+4=0 becomes y=x-1 so f(x)=x-1

Answer 2

I think you mean "function." Here is a simple function: d = 60t.

The d stands for distance in miles, t for time in hours. This function (formula) says distance is a function of time. The distance you travel at 60 miles an hours depends or is a function of the number of hours you travel. Functions are useful because you can put in a value for the variable on the right and get an answer for the one on the left. Put in t=10 hours above and you get the distance traveled is 600 miles.

So you want to solve each of your equations for y so that you can put in a value for x, do a calculation and get a value for y. You do this by adding and subtracting until the y term is alone on the left. Then divide (if necessary) to get y alone.

Here is the second one in detail:

4x + 2y = 14 To get 2y by itself subtract 4x from both sides

4x - 4x + 2y = 14 -4x and simplify to

2y = 14 - 4x Now y is multiplied by 2 so do the opposite

and divide both sides (every term) by 2 to get

2y/2 = 14/2 - 4x/2 which simplifies to

y = 7 - 2x or y = -2x + 7

Both answers are correct. We have written y as a function of x. This means we have a formula for calculating values of y just by putting numbers in for x such as 0,1,2,3,... and doing the arithmetic.

So when x = (-4), y = -2(-4) + 7 = 15.

We can say y=15 when x=-4. We can also write

y = f(x) = -2x + 7 and y = f(-4) = 15.

Now try the other two problems.

Answer 3

well, this is simple. all you need to know for this, is when writing in function form you are solving for y. so for the first one:

8X+Y-4=0
8X+Y=4
Y=4-8X

and then you have the function by switching y for f(x)
f(x)=4-8x

you see, function form is just asking for the function in terms of x only. so for the second and third one, solve for y and switch y with f(x)

you should get f(x) = 7-2x and f(x) =x-1 for the 2nd and third respectively

Answer 4

Is function form same as slope-intercept form, which means you have y = ax+b

y = -8x + 4
y = -2x + 7
y = x - 1