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.