Which representation has a constant of variation of –2.5?
A
x
–2
–3
–4
–5
y
–5
–7.5
–10
–12.5
B
x
4
6
8
10
y
–10
–15
–20
–25
C
y = negative 2.5 x + 1
D
On a coordinate plane, a line goes through points (negative 1, 0) and (0, negative 2).
A
B
C
D
C
To find the representation that has a constant of variation of -2.5, we need to look for an equation or relationship where the ratio of y to x is always -2.5.
Looking at the options:
A) The values of y decrease by 2.5 for every 1 decrease in x. So, the constant of variation here is -2.5.
B) The values of y decrease by 5 for every 2 increase in x. So, the constant of variation here is not -2.5.
C) The equation y = -2.5x + 1 does not have a constant of variation. The coefficient of x (-2.5) represents the slope, not the constant of variation.
D) The line going through points (-1, 0) and (0, -2) has a slope of (change in y / change in x) = (-2 - 0) / (0 - (-1)) = -2 / 1 = -2. This slope does not represent a constant of variation of -2.5.
Therefore, option A is the correct answer.