Question

What do the following two equations represent?

y=−x+5
5x+5y=20
A) The same line
B) Distinct parallel lines
C) Perpendicular lines
D) Intersecting, but not perpendicular lines

Answer 1

The two equations represent distinct parallel lines because they have the same slope of -1 but different y-intercepts (5 and 4 respectively).

Step-by-step explanation:

When analyzing the equations y = -x + 5 and 5x + 5y = 20, we first need to understand that these represent straight lines. To determine the relationship between these two lines, we need to transform the second equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Let's start by converting 5x + 5y = 20 into slope-intercept form: dividing every term by 5 gives us x + y = 4, and then solving for y gives us y = -x + 4. Now, we can clearly compare the slopes of the two lines. The first equation has a slope of -1, and the second equation, now in the form y = -x + 4, also has a slope of -1. Since both lines have the same slope but different y-intercepts, they are distinct parallel lines.

The answer to the question "What do the following two equations represent? y=-x+5 5x+5y=20" is B) Distinct parallel lines.