Find f(x)=ax+b, a linear function, in which f(2)=7 and f(-1)= -5?

Question

Can someone please explain this to me simply? I don't know anything about graphs or functions!

Answer 1

Given:
f(2) = 7
f(-1) = -5

Find: f(x) = ax + b

By definition,
f(2) = a(2) + b
f(2) = 2a + b, which in turn is given to be equal to 7.

f(-1) = a(-1) + b
f(-1) = -a + b = -5

Two equations, two unknowns are

2a + b = 7
-a + b = -5

We may solve this by subtracting the equations to eliminate b.

2a - (-a) = 7 - (-5)
2a + a = 12
3a = 12
a = 4

Now that we have a, b is easy to get.
2a + b = 7
2(4) + b = 7
8 + b = 7
b = -1

a = 4, b = -1, so the linear function is

f(x) = 4x - 1

Answer 2

f(x) represents the y value for a given x. So by the two equations you have two points (2,7) and (-1,-5) in the form (x,y). Slope is the rise/run where rise is the difference in the y values and run is the difference in the x values. Slope is generally show as the variable m.

In this case the difference in y is 7 - (-5) or 7 + 5 which is 12. The difference in x is 2 - (-1) or 2 + 1 which is 3. Therefore the slope m is 12/3 or 4.

In point slope form y - Y = m(x - X)

y - 7 = 12(x - 2)
y = 12x -24 +7
y = 12x - 17

Hope this helps!

Answer 3

If f(x)=ax+b; f(2) means the value of ax+b when x=2

And f(-1) means the value of ax+b when x= -1

So f(2)=a*2+b=2a+b and f(-1)=a*(-1)+b=-a+b

Given f(2)=7 and f(-1)= -5 which gives

2a+b=7 and -a+b= -5

solving these equation is easy and solution gives
a=4
b= -1

Answer 4

Simply substitute the value of x in the equation and solve.

Thus 2a + b = 7 and - a + b = - 5

Subtracting the second equation from the first, we get

3a = 12

a =4

Substituting in first equation

8 + b = 7

b = -1

So, f(x) = 4x - 1

Answer 5

hi....

f(2)=2a+b=7
f(-1)=-a+b=-5
so solving we get 3a =12 and a=4
this gives b=-1