Given f = 3x - m find m if the point (-1,-5) is on the line. For m = 2 find the point that is on the line and it has similar coordinates.

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

f=3x-3m.

Since the point (-1, -5) is on the line f = 3x-m, the point should satisfy f= 3x-m:

-5 = 3(-1)-m.

-5 = -3-m.

-5+3 = -m

-2= -m.

2 = m.

Therefore , f = 3x-2 . and m = 2.

Form  m= 2, to find the points that has similar coordinates:

Let  x= k and f = k be the similar points . Then (k,k) should be on f = 3x-2. So k = 3k-2.

k = 3k-2

k-3k = -2

-2k = -2.

k = -2/-2 = 1.

Therefore . (k,k) = (1,1) is the point having similar coordinates onthe line f = 3x-2.

Verification Put x= 1 and and f = 1 in f = 3x-2. Then 1 = 3*1-2 gives 1 = 1.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If the given point (-1,-5) belongs to the line y= 3x - m, then:

f(-1) = -5

f(-1) = 3*(-1) - m

f(-1) = -3 - m

-3 - m = -5

m = 5 - 3

m = 2

The equation of the line is:

y = 3x - 2

We'll note the point that has like coordinates and it belongs to the line y = 3x - 2 as M(n,n).

Since the point is located on the line y = 3x - 2, it's coordinates verify the expression of the line.

We'll put y = f(x) and we'll substitute x and y by the coordinates of the given point:

f(n) = 3n-2 (1)

But f(n) = n (2)

We'll conclude from (1) and (2) that:

3n-2 = n

We'll isolate n to the left side. For this reason, we'll subtract n both sides:

3n - n = 2

2n = 2

n = 1

The point located on the line y = 3x - 2 has the coordinates (1;1).

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