Let's solve the system of equations by graphing.

The two equations are:

1. $y = 2x - 2$
2. $x = 4$

Step 1: Graph $y = 2x - 2$

This is a linear equation in slope-intercept form, $y = mx + b$, where:

• $m = 2$ is the slope (rise over run),
• $b = -2$ is the y-intercept (the point where the line crosses the y-axis).

To graph:

• Start at the y-intercept, $(0, -2)$.
• From this point, use the slope $2$, which means for every 1 unit you move to the right (positive x direction), move 2 units up (positive y direction). So another point would be $(1, 0)$.
• Draw the line connecting these points.

Step 2: Graph $x = 4$

This is a vertical line where the value of $x$ is always 4, regardless of the value of $y$. To graph this:

• Draw a straight vertical line passing through $x = 4$.

Step 3: Find the Intersection Point

The solution to the system is where the two lines intersect. By graphing both equations, you will see that they intersect at the point $(4, 6)$.

So the solution to the system of equations is: $x = 4, \quad y = 6$

Would you like more details on any step?

Here are 5 related questions:

1. How do you find the slope from an equation in standard form?
2. What happens when two lines are parallel?
3. How can you determine if two lines are perpendicular?
4. How do you convert a linear equation from standard form to slope-intercept form?
5. How do you graph a horizontal line, like $y = 3$?

Tip: When graphing lines, always make sure to accurately plot key points, especially the intercepts, for a clearer solution.