How to Write an Equation for a Function By Andrea Hamilton; Updated April 24, In mathematics, an equation is an expression that equates two values on either side of an equal sign. From the equation, you can determine the missing variable.

Functions algebra Video transcript For a given input value b, the function f outputs a value a to satisfy the following equation 4a plus 7b is equal to negative So for a given input b, the function f, the function f will output an a that satisfies this relationship right over here for the a and the b.

Write a formula for f of b in terms of b. So we want to do, we just want to solve for -- if we're given a "b", what "a" does that imply that we have to output? Or another way to think about it is -- let's just solve for a, or we could think about a as being a function of b.

So let's write this. So we have 4a plus 7b -- is equal to negative So I can solve for a in terms of b, that any b that I have -- Let's say these b's are on the right hand side I can put it in.

I can substitute that value for b and I can just solve for a. I can solve for a that needs to be outputted. So let's do that. Let's solve for a. So I want to get all the a on I wanna just have an a leftover on the left hand side, and have everything else on the right hand side including the b's.

So let's get rid of this b on the left hand side. And I can do that by subtracting 7b. Of course I wanna do that to both sides. I can't just do an equation and do an operation only on one side like that. So let's subtract, and we are left with we are left with -- the 7b's add up to zero.

We're left with 4a is equal to negative 52 minus 7b, minus 7b.

Now, to isolate the a here, just to have an a here instead of 4a, we can divide both sides by 4. We can divide both sides by 4. So I'm gonna divide everything by 4.

And on the left hand side, we got our goal. We are left with an a is equal to -- Now what's negative 54 divided by -- What is the negative 52 divided by 4? So let's think about it. So it's gonna be So given a "b", if you give me a "b", I can put that value right over here, and I can calculate what the corresponding a needs to be in order to satisfy this relationship.

So if I want a formula for f of b in terms of b, I can say, look, you give me a "b", the output of our function, which is f of a.

So hopefully that helped.The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept..

If you know the slope (m) any y-intercept (b) of a line, this page will show you how to find the equation . plot the data, letting x = 0 correspond to the year , find a quadratic function that models the data,; plot the function on the graph with the data and determine how well the graph fits the data, ; use the model to predict the cumulative number of AIDS cases for the year Use a stylus or your finger to write a math equation by hand.

If you're not using a touch device, use your mouse to write out the equation. You can select portions of the equation and edit them as you go, and use the preview box to make sure Word is correctly interpreting your handwriting. Office has equations that you can readily insert into your documents.

If the Office built-in equations donâ€™t meet your needs, you can edit, change the existing equation, or write your own equation from scratch.

Choose Insert > Equation and choose the equation you want from the gallery. After you. Graphing Rational Functions. How to graph a rational function?A step by step tutorial. The properties such as domain, vertical and horizontal asymptotes of a rational function are also investigated.

Writing linear equations using the slope-intercept form. Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept. Example. Find the equation of the line. This gives us the linear function.

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