The problem asks to sketch the graph of each of the following four lines: 1. $y = -x - 2$

1. Problem Description

The problem asks to sketch the graph of each of the following four lines:

1. $y = -x - 2$

2. $y - 5 = 2$

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

4. $y = -\frac{1}{5}x + 4$

2. Solution Steps

1. For the first equation, $y = -x - 2$, we can identify the slope as $-1$ and the y-intercept as $-2$. We can plot the y-intercept at $(0, -2)$. Then using the slope, we can find another point. For example, if $x = 1$, then $y = -1 - 2 = -3$, so we have the point $(1, -3)$. Draw a line through these two points.

2. For the second equation, $y - 5 = 2$, we can add 5 to both sides to get $y = 7$. This is a horizontal line passing through $y = 7$.

3. For the third equation, $y = \frac{1}{2}x - 2$, we can identify the slope as $\frac{1}{2}$ and the y-intercept as $-2$. We can plot the y-intercept at $(0, -2)$. Then using the slope, we can find another point. For example, if $x = 2$, then $y = \frac{1}{2}(2) - 2 = 1 - 2 = -1$, so we have the point $(2, -1)$. Draw a line through these two points.

4. For the fourth equation, $y = -\frac{1}{5}x + 4$, we can identify the slope as $-\frac{1}{5}$ and the y-intercept as $4$. We can plot the y-intercept at $(0, 4)$. Then using the slope, we can find another point. For example, if $x = 5$, then $y = -\frac{1}{5}(5) + 4 = -1 + 4 = 3$, so we have the point $(5, 3)$. Draw a line through these two points.

3. Final Answer

1. $y = -x - 2$

2. $y = 7$

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

4. $y = -\frac{1}{5}x + 4$