Devon needs to come up with ordered pairs that make up the line for this linear equation 3y − 3x = 12?  Which ones would work?

(1,5) (2,6) (5,11)

(0,4) (2,6) (3,9)

(1,5) (2,6) (4, 9)

(0,4) (1,5) (2,6)

To determine which set of ordered pairs makes up the line for the given linear equation \(3y - 3x = 12\), we should first solve the equation for \(y\).

### Step 1: Simplify the equation
\[
3y - 3x = 12
\]
Divide every term by 3:
\[
y - x = 4
\]
Add \(x\) to both sides:
\[
y = x + 4
\]

This is the equation of the line in slope-intercept form \(y = x + 4\).

### Step 2: Check each set of ordered pairs to see which ones satisfy \(y = x + 4\).

#### First set: \((1,5)\), \((2,6)\), \((5,11)\)
- For \((1,5)\): \(5 = 1 + 4\) (True)
- For \((2,6)\): \(6 = 2 + 4\) (True)
- For \((5,11)\): \(11 = 5 + 4\) (True)

This set works.

#### Second set: \((0,4)\), \((2,6)\), \((3,9)\)
- For \((0,4)\): \(4 = 0 + 4\) (True)
- For \((2,6)\): \(6 = 2 + 4\) (True)
- For \((3,9)\): \(9 = 3 + 4\) (False, \(9 \neq 7\))

This set does not work.

#### Third set: \((1,5)\), \((2,6)\), \((4,9)\)
- For \((1,5)\): \(5 = 1 + 4\) (True)
- For \((2,6)\): \(6 = 2 + 4\) (True)
- For \((4,9)\): \(9 = 4 + 4\) (False, \(9 \neq 8\))

This set does not work.

#### Fourth set: \((0,4)\), \((1,5)\), \((2,6)\)
- For \((0,4)\): \(4 = 0 + 4\) (True)
- For \((1,5)\): \(5 = 1 + 4\) (True)
- For \((2,6)\): \(6 = 2 + 4\) (True)

This set works.

### Conclusion
The sets of ordered pairs that satisfy the equation are:

- \((1,5)\), \((2,6)\), \((5,11)\)
- \((0,4)\), \((1,5)\), \((2,6)\)

Would you like further details or have any questions?

### Related Questions
1. How do you convert a linear equation from standard form to slope-intercept form?
2. What is the geometric interpretation of the slope-intercept form of a line?
3. How can you determine if a point lies on a given line?
4. What are the key differences between solving for a line in slope-intercept form vs. standard form?
5. How can you graph a line given its equation in slope-intercept form?

### Tip
To quickly verify if a point lies on a line, substitute the point's coordinates into the equation and see if the equation holds true.

Devon needs to come up with ordered pairs that make up the line for this linear equation 3y − 3x = 12? Which ones would work?

(1,5) (2,6) (5,11)

(0,4) (2,6) (3,9)

(1,5) (2,6) (4, 9)

(0,4) (1,5) (2,6)

Discover how to find ordered pairs that satisfy the linear equation 3y − 3x = 12. This problem involves key algebraic concepts, including the conversion of the equation to slope-intercept form and checking pairs against it. Ideal for students in Grades 8-10.

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