For the data in each table tell whether y varies directly with x if it does write an equation for the direct variation x|y
-3|-7.5
-1|2.5
2|-5
5|-12.5
If only the first one were
-3 | +7.5
it would work with y = -2.5 x
However as it is written he slope is NOT constant
yes, y varies directly with x.
y=4x is an equation of the Direct Variation
Step-by-step explanation:
x y
0 0
1 4
2 8
3 12
From the above data:
we can say that y varies directly with x.
Direct variation states that if y is expressed as the product of some constant number k and x.
i.e y=kx
Now, let any points from above data x= 2 and y= 8 to calculate the value of k,
8=2k
⇒
Therefore, the equation for the direct variation is, y=4x
To determine whether y varies directly with x, we need to check if there is a constant ratio between the values of y and x.
Let's calculate the ratio of y to x for each pair of values:
For the first pair (-3, -7.5):
y / x = (-7.5) / (-3) = 2.5
For the second pair (-1, 2.5):
y / x = (2.5) / (-1) = -2.5
For the third pair (2, -5):
y / x = (-5) / 2 = -2.5
For the fourth pair (5, -12.5):
y / x = (-12.5) / 5 = -2.5
Since the ratio of y to x is the same for all pairs of values (-2.5), we can conclude that y varies directly with x.
The equation for the direct variation is:
y = kx
To find the value of k (the constant of variation), we can use any pair of values. Let's use the first pair (-3, -7.5):
-7.5 = k(-3)
Solving for k:
k = -7.5 / -3 = 2.5
Therefore, the equation for the direct variation is:
y = 2.5x
To determine whether the variable y varies directly with x, we need to check if the ratios between y and x remain constant. If the ratios are constant, then y varies directly with x.
Let's calculate the ratios for each pair of x and y values:
For the first pair (-3, -7.5), the ratio is y/x = -7.5/-3 = 2.5.
For the second pair (-1, 2.5), the ratio is y/x = 2.5/-1 = -2.5.
For the third pair (2, -5), the ratio is y/x = -5/2 = -2.5.
For the fourth pair (5, -12.5), the ratio is y/x = -12.5/5 = -2.5.
Since the ratios are consistent and equal to -2.5 for all pairs of x and y values, we can conclude that y varies directly with x.
The equation for direct variation is of the form y = kx, where k is the constant of variation. In this case, since the ratio is -2.5, the equation would be y = -2.5x.