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Another way to answer this question is that you know any linear function can always be written y = mx + b, where m is the slope.
Find m first, (4 - 3)/(2 - -1)=1/3.
Then plug in one point to solve for b, 4 = (1/3)(2) + b, solve for b and b = 10/3.
Replace m and b with their values, and y = (1/3)x + (10/3).
Here is another example where we find the equation of a line from two points:
The general form of a linear function is
f(x)=ax + b
So, f(-1)=3 means that we hhave to substitute, in the general form, the unknown x with the value -1.
-1xa + b = 3
We'll do the same thing with the following f(2)=4
2a +b = 4
Now, in order to find the function f, we have to determine the unknown coefficients a and b.
SO, we'll subtract from the last relation, 2a +b = 4, the anterior one ,-a + b= 3.
2a +b - (-a) +b = 4-3
3a = 1
a = 1/3
With the known value of a, we are going in any of the both anterior relation, substitute a and find out the value of b unknown.
We choose the relation -a + b =3, beccause it's more simple to calculate b, after substituting a value.
-1/3 + b = 3
b = 3 + 1/3
The common denominator is 3, so we have to multiply the first term 3, with the common denominator 3
b = ( 9 +1)/3
b = 10/3
Now we could write down the linear function f.
f(x) = (1/3)x + 10/3
General equation of linear function f is:
Since f(-1)=3, so we have to subsitute x=-1
-m+c=3 -eqn 1
Also, f(2)=4, so we have to sub. x=2
2m+c=4 -eqn 2
Subtract eqn 1 from eqn 2
subsitute m=1/3 into eqn 2
= 10/3 or 3 1/3
The equation of f(x): 1/3 x+10/3 (mx+c)
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