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.
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.
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.
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).