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
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
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)=2 => -3a+b=2 (1)
B belongs to the Graphic of f(x)if only f(-4)=5
f(-4)=5=> -4a+b=5 (2)
By subtracting the relation (2) from the relation (1), we'll have:
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