Question 4 (Multiple Choice, 4 points) (08.02) Which of the following graphs best represents the solution to the following system of equations? y = −2x + 2 y = 2x + 2

To find which graph best represents the solution to the system of equations, we need to consider the characteristics of each equation and where they would intersect on the coordinate plane.

The system of equations is:

1. \( y = -2x + 2 \) 2. \( y = 2x + 2 \)

Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The slope tells you how the line tilts and the y-intercept is where the line crosses the y-axis.

Looking at the slopes of each line: - The first equation has a slope of -2, which means the line will go down two units for every one unit it goes to the right. Its y-intercept is +2, so it will cross the y-axis at (0,2). - The second equation has a positive slope of 2, which means the line will go up two units for every one unit it goes to the right. Its y-intercept is also +2, so it will also cross the y-axis at (0,2).

The slopes are opposite reciprocals of each other. This means the two lines are perpendicular, and since they have the same y-intercept, they will cross each other at that point. The intersection point (thus, the solution to the system of equations) is at the point where x equals zero and y equals 2, which is (0, 2).

The correct graph would show two perpendicular lines intersecting at the point (0, 2).