# Find the function y = mx + n if the points (1;2) and (-1;-1) are on the graph of the function.

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y = mx+n, the points (1,2) and (-1,-1) are on the graph.

Since points are on the graph, the coordinates of the two given points should satisfy the graph.

Point (1,2) is on y = mx+n. So m*1+n= 2. Or

m+n = 2....(1)

Point (-1, -1) is on the graph y mx+n . So m*(-1) +n = -1, Or

-m+n = -1....(2).

Adding eq(1) and eq (2) , we get:

m+n-m+n = 2-1 = 1.

2n = 1.

n = 1/2.

Eq(1) -eq(2) gives: m+n - (m+n) = 2- (-1) = 3.

2m = 3.

m = 3/2.

Therefore the value of m = 1/2 and n = 3/2.

The function that has to be determined is a linear function. A linear function is determined when it's coefficients are determined.

y = f(x) = mx + n

So, in order to determine y, we'll have to calculate the coefficients m and n.

Since the function is determined by the points (1,2) and (-1,-1), that means that if we'll substitute the coordinates of the points into the expression of the function, we'll get the relations:

f(1) = 2

f(1) = m*1 + n

m + n = 2 (1)

f(-1) = -1

f(-1) = m*(-1) + n

-m + n = -1 (2)

We'll add (1) and (2):

m + n -m + n = 2 - 1

We'll combine and eliminate like terms:

2n = 1

**n = 1/2**

We'll substitute n in (1):

m + n = 2

m + 1/2 = 2

m = 2 - 1/2

**m = 3/2**

**The expression of the linear function is:**

**f(x) = 3x/2 + 1/2**