# Having the function f(x)=ax+b which passes through the points A(-3,2) B(-4,5) and c=b-a, then which is the value of C ?

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a) finding f(x)=ax+b given two points A(-3,2) and B(-4,5);

b) finding c=b-a answer exercise a) then b) goes without saying-

Answer to a) slope a or m, m=Y2-Y1/X2-X1

m=[5-2]/[-4-(-3)]

m=-3

now using the intercept F.:Y-Y1= m (X-X1) and computing one of the two points with the slope m will get Y=F(X)=-3X-7

THEREFORE, C=-4 WHEN b Is -7 and a is -3.

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When a line having function

f(x) = ax + b ... (1)

passes through two points A(x1, y1) and B(x2, y2), the value of a is given by:

a = (y2 - y1)/(x2 - x1) ... (2)

As per the question the values of the coordinates of the points A and B are:

x1 = -3 and y1 = 2

x2 = -4 and y2 = 5

Substituting these values in equation (2) we get:

a = (5 - 2)/[-4 - (-1)}] = 3/-1 = -3

substituting this value of a and of x1, and y1 in equation (1) we get:

2 = -3*(-3) + b

Therefor: 2 = 9 + b

Or:

b = -7

It is given:

c = b - a

Substituting values of a and b in above equation we get:

c = -7 - (-3) = -4

Answer: c = -4

The slope of the line passing through A(-3,2) and B(-4,5) is

(5-2)/(-4-(-3)) = 3/-1 = -3.

Therefore, the slope of f(x) = -3. or a = -3.

Since f(x) = -3x+b passes through A,

-3(-3)+b = 2 or b = 9+2 =11. Therefore,

b-a = 11-(-3) = 14

If the function passes through the points mentioned, that means that the coordinates of the points,substituted in the expression of the function, verifies it, so:

A belongs to the Graphic of f(x)if only f(-3)=2

f(-3)=-3a+b

f(-3)=2 => **-3a+b=2 (1)**

B belongs to the Graphic of f(x)if only f(-4)=5

f(-4)=-4a+b

f(-4)=5=> **-4a+b=5 (2)**

By subtracting the relation (2) from the relation (1), we'll have:

-3a+b+4a-b=2-5

**a=-3**

With the known value for a, we'll go into the relation (1) (or (2)), to find out the value for b.

-3a+b=2 => -3(-3)+b=2 =>b=2+9

**b=11**

c=b-a

c=11-(-3)

**c=14**