Let's graph the two equations and find at least three ordered pairs that satisfy each.

1. $x + y = 3$

To graph this equation, we can rewrite it in slope-intercept form ($y = mx + b$):

$y = -x + 3$

This tells us that the slope is $-1$ and the y-intercept is $3$, so the line crosses the y-axis at $(0, 3)$.

Find 3 ordered pairs:

• When $x = 0$, $y = 3$ (so, one point is $(0, 3)$).
• When $x = 1$, $y = 3 - 1 = 2$ (so, another point is $(1, 2)$).
• When $x = -1$, $y = 3 - (-1) = 4$ (so, another point is $(-1, 4)$).

So, the ordered pairs are: $(0, 3), (1, 2), (-1, 4)$

2. $2x - y = 8$

Let's also solve this for $y$ to get it in slope-intercept form:

$y = 2x - 8$

This tells us the slope is $2$ and the y-intercept is $-8$, so the line crosses the y-axis at $(0, -8)$.

Find 3 ordered pairs:

• When $x = 0$, $y = -8$ (so, one point is $(0, -8)$).
• When $x = 2$, $y = 2(2) - 8 = 4 - 8 = -4$ (so, another point is $(2, -4)$).
• When $x = 4$, $y = 2(4) - 8 = 8 - 8 = 0$ (so, another point is $(4, 0)$).

So, the ordered pairs are: $(0, -8), (2, -4), (4, 0)$

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Would you like me to go ahead and graph these equations for you, or do you have any questions about the process? Also, let me know if you'd like more examples!

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Additional Related Questions:

1. How do you find the slope and y-intercept of an equation in standard form?
2. How do you graph a linear equation when given only two points?
3. What is the significance of the slope and y-intercept in the context of real-life situations?
4. How can you determine if two lines are parallel or perpendicular from their equations?
5. What happens when the slope of an equation is zero or undefined?

Tip:

If you're ever unsure about a graph, plotting at least two points will give you a clear idea of the line's direction.