To graph the line $y = -x + 5$ using the provided table of values, let's interpret the table as coordinates to be plotted on a Cartesian plane.

Each pair of $x$ and $y$ values represents a point $(x, y)$ on the line $y = -x + 5$.

The values given in the tables are:

Table 1:

• $(-10, 15)$
• $(-9, 14)$
• $(-8, 13)$
• $(-7, 12)$
• $(-6, 11)$
• $(-5, 10)$
• $(-4, 9)$

Table 2:

• $(-3, 8)$
• $(-2, 7)$
• $(-1, 6)$
• $(0, 5)$
• $(1, 4)$
• $(2, 3)$
• $(3, 2)$

Table 3:

• $(4, 1)$
• $(5, 0)$
• $(6, -1)$
• $(7, -2)$
• $(8, -3)$
• $(9, -4)$
• $(10, -5)$

Instructions to Graph the Line

1. Plot each of these points on a graph with an $x$-axis and $y$-axis.
2. The line $y = -x + 5$ should pass through all these points because they are solutions to the equation.
3. After plotting, draw a straight line connecting the points to illustrate the linear relationship.

Would you like me to plot the graph for you, or do you have questions about the steps?

Here are some questions to deepen your understanding:

1. How would the line change if the equation was $y = -x + 3$ instead?
2. What does the slope $-1$ tell us about the direction of the line?
3. If the equation were $y = x + 5$, how would the line's direction differ?
4. What would happen if we changed the equation to $y = -2x + 5$?
5. How can we determine the y-intercept just by looking at the equation $y = -x + 5$?

Tip: The coefficient of $x$ (in this case, $-1$) represents the slope, which determines the angle and direction of the line on the graph.