To solve the system of equations by graphing, we need to graph both equations and find their intersection point, which will represent the solution to the system.

Given equations:

1. $y = -x - 6$
2. $y = 2x$

Step 1: Graph the first equation $y = -x - 6$

• The slope is $-1$ and the y-intercept is $-6$.
• Plot the y-intercept at $(0, -6)$.
• Using the slope $-1$, move 1 unit down and 1 unit to the right to get another point $(1, -7)$, or alternatively move 1 unit up and 1 unit to the left to plot $(-1, -5)$.
• Draw the line through these points.

Step 2: Graph the second equation $y = 2x$

• The slope is $2$ and the y-intercept is $0$.
• Plot the y-intercept at $(0, 0)$.
• Using the slope $2$, move 2 units up and 1 unit to the right to get another point $(1, 2)$, or move 2 units down and 1 unit to the left to plot $(-1, -2)$.
• Draw the line through these points.

Step 3: Identify the intersection point

• By graphing both lines, the point where the two lines intersect is the solution to the system.
• The lines intersect at the point $(-2, -4)$.

Solution:

The solution to the system of equations is $(-2, -4)$.

Do you want more details or have any questions? Here are five related questions:

1. How do you find the slope and intercept from an equation in slope-intercept form?
2. Can you explain what the intersection of two lines represents in terms of systems of equations?
3. What happens if two lines are parallel in a system of equations?
4. How would you graph a line given its slope and a point that lies on it?
5. What is the significance of a slope being positive or negative?

Tip: When graphing linear equations, always start by plotting the y-intercept and use the slope to determine other points on the line.