Question

The equations of four lines are given. identify which lines are parallel. line

A: y=8x−5y=8x-5 line
B: x 16y=−5x 16y=-5 line
C: y=−6x−7y=-6x-7 line
D: y 3=18(x−1)

Answer 1

To determine which lines are parallel, we compare their slopes. Lines A, C, and D have slopes of 8, -6, and 18, respectively. Since none of them share the same slope, none of the lines are parallel.

Step-by-step explanation:

To identify which of the given lines are parallel, we must look at the slope of each line, since parallel lines have identical slopes. The standard form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

For Line A (y=8x-5), the slope is 8. Line B is not written in standard form, and cannot be assessed here. For Line C (y=-6x-7), the slope is -6. For Line D, once simplified, we can see that the slope is 18 as it is given by y 3=18(x-1), which simplifies to y=18x-15 when the 3 is moved to the right-hand side of the equation and the expression is expanded.

With slopes of 8, -6, and 18, none of these lines are parallel because no two slopes are equal.