i need help for solving the linear function f with values f(1) = 6 and f(-2) = -3

Question

i need to turn that into y = mx + b and f(x) =

Answer 1

So to start off, let's just think about the information we have on hand.

You know we want set-up two types of equations:

y = mx + b

and

f(x) = ?

We also have f(1) = 6 and f(-2) = -3

One important thing to note is that f(x) really is just y.

It means you're plugging in x into some function and getting some output out of it...and that output? y!

Now with that in mind, let's try figuring out what we're missing.

y = mx + b, we want to figure out m and b.

Well, to start we could try plugging in our values for x and y given.

For f(1) = 6, we get:

6 = m(1) + b

as y = 6 and x = 1

For f(-2) = -3, we get:

-3 = m(-2) + b

We have two variables and two equations...I think we can solve for them :)

The way I'll go about it is to maybe see what variable I can isolate. Let's try setting the equations equal to each other.

We can do this by subtracting 6 from both sides on our first equation giving us:

6 - 6 = m + b - 6

0 = m + b - 6

For the second we can add 3 to both sides

-3 + 3 = -2m + b + 3

0 = -2m + b + 3

We can then set them equal to each other on the 0 side:

m + b - 6 = -2m + b + 3

Although our m's are different, it looks like we can subtract b from both sides, isolating one variable!

m - 6 = -2m + 3

We then solve for m by isolating it

3m = 9

m = 3

Great! We have one variable. y = 3x + b...almost there.

Lets plug in one of our f() values given into the equation (doesnt matter which one):

I'll do f(1) = 6

6 = 3(1) + b

6 = 3 + b

b = 3

Awesome!!!

Now we finally have our form:

y = 3x + 3

which is f(x) = 3x + 3

And we can double check if we want to be extra sure:

Lets plug in x = 1 and x = -2

y = 3(1) + 3 = 6

y = 3(-2) + 3 = -3

Which makes sense, since f(1) = 6 and f(-2) = -3 !!!!

So we know we have the right answer :)

Answer 2

Let, f(x) = mx + b. Here y is f(x) which is a function of x. To turn into y = mx + b form, we have to find m and c first. Now substitute x values to f(x) as below.

f(1) = m*(1) + b = m + b

f(-2) = m* (-2) + b = -2m + b

We have two equations. We know the values of f(1) = 6 and f(-2) = -3. Therefore above two equations are now,

m + b = 6 -------------------- 1

-2m + b = -3 ------------------- 2

Now we solve these two equations and find values for m and b.

Solve for m : Eq.1 - Eq. 2

m - (-2m) = 6 - (-3)

3m = 9

m = 3

Solve for b: Substitute m value to Eq. 1:

3 + b = 6

b = 3

Therefore the answer is:

y = 3x + 3

Answer 3

(1,6) and (-2,-3) have a line through them with the equation

(6+3/(1+2) = (y+3)/(x+2)

9/3 = 3 = (y+3)/(x+2)

y+3 = 3x+6

y= 3x +6-3

y

= f(x) = 3x+3 in slope intercept form.

slope=m=3 = the coefficient of the x term.

intercept =b = 3 = the constant term = the point (0,3)

check the solution by plugging in the two points

6=3(1)+3

-3= 3(-2)+3

Answer 4

Hi Oje! Since f(x) is linear, it takes the form f(x) = mx + b.

Based on the 2 values of f you are given, you can have a system of 2 equations with 2 unknowns (m and b) and you can solve for m and b.

Because f(1) = 6, you can write: f(1) = m + b = 6

Because f(-2)= -3, you have: f(-2) = -2*m + b = -3

Now if you substract these 2 equations, you get: 3 *m = 9, thus m = 3

Since m + b = 6, you have b = 3.

Thus f(x) = 3*x+ 3

Do not forget to check your work and that the initial conditions given in the problem are satisfied.