Question

Identify which table shows a direct variation

Answer 1

You can tell if it has direct variation by finding the slope and inserting it and the coordinates into point slope form.

You can find the slope by putting both sets of coordinates into the equation
y - y / x -x , where the first y and x are from one set of coordinates, and the next two are from the other set.

(7.5 - 3) / (11.25 - 4.5)
4.5 / 6.75
The slope is 2/3

Next, input the slope and the origin (0,0) into point-slope form.
y - y = m (x - x)                 Substitute.
y - 3 = 2/3 (x - 4.5)            Distributive Property.
y - 3 = 2/3x - 8/15             Add 3 to both sides.
y = 2/3x + 37/15                Simplify.
y = 2/3x + 2 2/15   

So you know that the line does not go through origin, because its y-intercept is 2 2/15.

For the second one do the same things.

y -y / x - x
(3 - 1.5) / (12 - 8)
1.5 / 4
3/8

y - y = m ( x - x )
y - 3 = 3/8 (x - 12)
y - 3 = 3/8x - 24/8
y = 3/8x - 0
y = 3/8x

So the second one goes through the origin because its y-intercept is 0. The answer is Table 2 has direct variation.

Answer 2

Answer:

You can tell if it has direct variation by finding the slope and inserting it and the coordinates into point slope form.

You can find the slope by putting both sets of coordinates into the equation

y - y / x -x , where the first y and x are from one set of coordinates, and the next two are from the other set.

(7.5 - 3) / (11.25 - 4.5)

4.5 / 6.75

The slope is 2/3

Next, input the slope and the origin (0,0) into point-slope form.

y - y = m (x - x)                 Substitute.

y - 3 = 2/3 (x - 4.5)            Distributive Property.

y - 3 = 2/3x - 8/15             Add 3 to both sides.

y = 2/3x + 37/15                Simplify.

y = 2/3x + 2 2/15   

So you know that the line does not go through origin, because its y-intercept is 2 2/15.

For the second one do the same things.

y -y / x - x

(3 - 1.5) / (12 - 8)

1.5 / 4

3/8

y - y = m ( x - x )

y - 3 = 3/8 (x - 12)

y - 3 = 3/8x - 24/8

y = 3/8x - 0

y = 3/8x

So the second one goes through the origin because its y-intercept is 0. The answer is Table 2 has direct variation.

Step-by-step explanation: