Which graph represents the solution to the given system? y = –5x – 2 y + 2 = –5x (1 point) Responses Image with alt text: A coordinate plane with 2 linear equations graphed which are overlapping lines. Image with alt text: A coordinate plane with 2 linear equations graphed which are parallel lines. Slope of the lines is negative 5. The first line passes through the points left-parenthesis 0 comma negative 2 right-parenthesis and left-parenthesis 1 comma 4 right-parenthesis. The second line passes through the points left-parenthesis 0 comma negative 2 right-parenthesis and left-parenthesis negative 1 comma 4 right-parenthesis. The coordinate left-parenthesis 0 comma negative 2 right-parenthesis is written below the coordinate plane. Image with alt text: A coordinate plane with 2 linear equations graphed. Intersection of the lines is at (0, negative 2). The first line passes through the points left-parenthesis 0 comma negative 2 right-parenthesis and left-parenthesis 1 comma 4 right-parenthesis. The second line passes through the points left-parenthesis 0 comma negative 2 right-parenthesis and left-parenthesis negative 1 comma 4 right-parenthesis. The coordinate left-parenthesis 0 comma negative 2 right-parenthesis is written below the coordinate plane.
The correct graph that represents the solution to the given system is the first option:
Image with alt text: A coordinate plane with 2 linear equations graphed which are overlapping lines.
The correct graph that represents the solution to the given system is the one described in the third image. It shows a coordinate plane with two linear equations graphed, with the intersection point at (0, -2). The first line passes through the points (0, -2) and (1, 4), and the second line passes through the points (0, -2) and (-1, 4).
To determine which graph represents the solution to the given system of equations, we need to examine the characteristics of the system.
The given system is:
1) y = -5x - 2
2) y + 2 = -5x
Both equations are in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.
Looking at the slopes of the equations:
1) Slope of the first equation: -5
2) Slope of the second equation: -5
Since the slopes of both equations are the same (-5), this indicates that the lines are parallel to each other.
Now let's examine the y-intercepts of the equations:
1) y-intercept of the first equation: -2
2) y-intercept of the second equation: 2
The y-intercepts of the equations are different, which means the lines are not overlapping.
Based on the information above, we can conclude that the correct graph representation is the one that shows parallel lines. Therefore, the graph that represents the solution to the given system is the one described as "A coordinate plane with 2 linear equations graphed which are parallel lines. Slope of the lines is negative 5. The first line passes through the points (0, -2) and (1, 4). The second line passes through the points (0, -2) and (-1, 4)."