select all the points that are on the graph of the equation 4y - 6x = 12
a. (-4,-3)
b. (-1, 1.5)
c. (0, -2)
d. (0,3)
e. (3, 4)
f. (6,4)

The only points that a valid points on the graph of 4y - 6x = 12 are;

Option A; (-4,-3)

Option B; (-1, 1.5)

Option D; (0,3)

We are given the equation;

4y - 6x = 12

Let us make y the subject to get;

4y = 12 + 6x

y = (12 + 6x)/4

y = 3 + ³/₂x

Option A; at (-4, -3), let us put -4 for x to see if we will get y as -3;

y = 3 + ³/₂(-4)

y = 3 - 6

y = -3

Thus, (-4, -3) is a valid point

Option B; at (-1, 1.5)

y = 3 + ³/₂(-1)

y = 3 - 1.5

y = 1.5

Thus, (-1, 1.5) is a valid point

Option C; at (0, -2)

y = 3 + ³/₂(0)

y = 3

Thus, (0, -2) is not a valid point

Option D; at (0, 3)

y = 3 + ³/₂(0)

y = 3

Thus, (0, 3) is a valid point

Option E; At (3, 4)

y = 3 + ³/₂(3)

y = 3 + 4.5

y = 7.5

Thus; (3, 4) is not a valid point

Option F; At (6, 4)

y = 3 + ³/₂(6)

y = 3 + 9

y = 12

Thus, (6, 4) is not a valid point

In conclusion the only valid points are; (-4, -3), (-1, 1.5), (0, 3)

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b. (-1, 1.5)

d. (0,3)

Step-by-step explanation:

we have

we know that

If a ordered pair is on the graph of the linear equation, the the ordered pair must satisfy the linear equation

Verify each case

case a) we have

(-4,3)

substitute the value of x and the value of y in the equation

----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case b) we have

(-1,1.5)

substitute the value of x and the value of y in the equation

----> is true

The ordered pair satisfy the equation

therefore

The ordered pair is  on the graph of the linear equation

case c) we have

(0,-2)

substitute the value of x and the value of y in the equation

----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case d) we have

(0,3)

substitute the value of x and the value of y in the equation

----> is true

The ordered pair  satisfy the equation

therefore

The ordered pair is on the graph of the linear equation

case e) we have

(3,4)

substitute the value of x and the value of y in the equation

----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

case f) we have

(6,4)

substitute the value of x and the value of y in the equation

----> is not true

The ordered pair not satisfy the equation

therefore

The ordered pair is not on the graph of the linear equation

gregory's graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.