Question

Draw the graph of the pair of linear equations given below and then state whether the lines are parallel or perpendicular: 

2x + y = 5 and 2x + y = 7 

Answer 1

To graph the system of linear equations 2x + y = 5 and 2x + y = 7, we first rewrite them in slope-intercept form y = mx + b:

1. For the first equation:

2x + y = 5

⇒ y = –2x + 5

Slope (m): –2

y-intercept (b): 5 the point (0, 5)

2. For the second equation:

2x + y = 7

⇒ y = –2x + 7

Slope (m): –2

y-interept (b): 7 the point (0, 7)

The graph below shows the two lines plotted on a cartesian plane.

Analysis

Parallel Lines: Two lines are parallel if they have the same slope but different y-intercepts. Both equations have a slope of –2, but their y-intercepts are different (5 vs. 7). As shown in the graph, the lines never intersect. 

Perpendicular Lines: Two lines are perpendicular if the product of their slopes is –1. Since their slopes are identical (–2 × –2 = 4 ≠ –1), they are not perpendicular.

The lines represented by the equations 2x + y = 5 and 2x + y = 7 are parallel to each other.