Let's go through each of these equations and rewrite them in the form $y = mx + b$ (slope-intercept form), so they can be easily graphed:

16. $y = x + 2$

• Slope $m = 1$
• Y-intercept $b = 2$

This line has a slope of 1, meaning it rises 1 unit for every 1 unit it moves to the right. It crosses the y-axis at 2.

18. $y = \frac{1}{2}x - 1$

• Slope $m = \frac{1}{2}$
• Y-intercept $b = -1$

This line has a slope of $\frac{1}{2}$, meaning it rises 1 unit for every 2 units it moves to the right. It crosses the y-axis at -1.

20. $y - 3 = \frac{1}{3}(x - 3)$

First, solve for $y$: $y = \frac{1}{3}(x - 3) + 3$ Distribute: $y = \frac{1}{3}x - 1 + 3 = \frac{1}{3}x + 2$

• Slope $m = \frac{1}{3}$
• Y-intercept $b = 2$

This line has a slope of $\frac{1}{3}$, meaning it rises 1 unit for every 3 units it moves to the right. It crosses the y-axis at 2.

22. $y + 4 = (x - 5)$

First, solve for $y$: $y = (x - 5) - 4 = x - 9$

• Slope $m = 1$
• Y-intercept $b = -9$

This line has a slope of 1 and crosses the y-axis at -9.

Do you want to go through the graphing process in more detail or have any specific questions on these lines?

Here are five related questions:

1. How do you calculate the slope of a line from two points?
2. What does the slope represent in real-world applications?
3. How can you find the x-intercept of a line?
4. What happens to the graph of a line when you change its slope?
5. How does changing the y-intercept affect the position of the line?

Tip: Always check if a line passes through the origin by setting $x = 0$ and solving for $y$.