Question

What do the following two equations represent?

5x + y = 3
10.2 + 2y = -6
A. The same line
B. Distinct parallel lines
C. Perpendicular lines
D. Intersecting, but not perpendicular lines

Answer 1

The given equations represent distinct parallel lines.

Step-by-step explanation:

The given equations are:

1. 5x + y = 3

2. 10.2 + 2y = -6

To determine what these equations represent, we need to analyze their slope and y-intercept values.

1. The equation 5x + y = 3 can be rewritten as y = -5x + 3. This is in the form y = mx + b, where m represents the slope and b represents the y-intercept. The slope of -5 indicates a steep downward slope, and the y-intercept of 3 indicates that the line crosses the y-axis at the point (0, 3).

2. The equation 10.2 + 2y = -6 can be rewritten as 2y = -16.2, and further simplified as y = -8.1. This is a horizontal line with a slope of 0, and it intersects the y-axis at the point (0, -8.1).

Based on the analysis, the two equations represent distinct parallel lines.