124k views
3 votes
Determine whether the pair of lines is parallel, perpendicular, or neither. The equations are:

10 + 3x = 5y
5x + 3y = 1

a) Parallel
b) Perpendicular
c) Neither

1 Answer

5 votes

Final answer:

The pair of lines represented by the given equations is neither parallel nor perpendicular.

Step-by-step explanation:

To determine whether the pair of lines is parallel, perpendicular, or neither, we need to compare their slopes. The given equations are:

10 + 3x = 5y

5x + 3y = 1

To compare their slopes, we need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Comparing the slopes, we can determine whether the lines are parallel, perpendicular, or neither.

Let's find the slope-intercept form for the first equation:

10 + 3x = 5y

3x - 5y = -10

-5y = -3x - 10

y = (3/5)x + 2

The slope of the first line is 3/5.

Now, let's find the slope-intercept form for the second equation:

5x + 3y = 1

3y = -5x + 1

y = (-5/3)x + 1/3

The slope of the second line is -5/3.

Since the slopes of the lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular. Hence, the answer is c) Neither.

User Bernard Covic
by
7.2k points