Determine whether the lines are parallel or perpendicular. Explain your answer. 2y=16+4x2y=16+4x 6y-30=12x6y−30=12x

Answer 1

Assuming the two equations are:

2y = 16 + 4x & 6y - 30 = 12x

NOTES:

When two lines are parallel, their slopes are the same.

e.g.,

m₁ = 2/3

m₂ = 2/3

When two lines are perpendicular, their slopes are negative reciprocals of each other.

e.g.,

m₁ = 2/3

m₂ = -3/2

SOLVE:

In order to answer this questions, put each equation in the slope-intercept form, y = mx + b, then compare their slopes.

for 2y = 16 + 4x

y = 2x + 8

for 6y - 30 = 12x

y = 2x + 5

ANSWER:

because both functions have the same slope of 2/1, the lines are parallel.

notice: the only difference between the two functions is they have different y-intercepts of 8 and 5, respectively. If they had the same slope and the same y-intercept, they would in fact represent the same line.