Points and linesGiven 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 .
You should remember that a point belongs to a line if replacing coordinates of point for x and y, in equation of line, it holds.
Hence, you need to replace -`1` for `x` and -`5` for y in equation of function `y = 3x - m` , such that:
`-5 = 3*(-1) - m => -5 + 3 = -m => -2 = -m => m = 2`
Hence, evaluating m, under the given conditions, yields `m = 2` .
You need to find a point that belongs to the line y = 3x - 2 whose coordinates are equal, `x = y` , such that:
`x = 3x - 2 => x - 3x = -2 => -2x = -2 => x = 1 => y = 1`
Hence, evaluating the equal coordinates of the point that belongs to the line `y = 3x - 2` , yields `x = y = 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).