Question

Dentify which lines are parallel.

a) y = -7x + 6
b) x + (1/3)y = -6
c) y = -5x - 8
d) y + 7 = -(x + 4)

Answer 1

After converting all equations to slope-intercept form, we determined that none of the lines have matching slopes, indicating that there are no parallel lines among the given options.

Step-by-step explanation:

To identify which lines are parallel, we need to compare their slopes. Parallel lines have identical slopes. Given equations of lines in different forms, we must rearrange them into slope-intercept form (y = mx + b) where m represents the slope.

• Equation a is already in the slope-intercept form with a slope of -7.
• Equation b can be rearranged to slope-intercept form by solving for y: y = -(3)x - 18, which has a slope of -3.
• Equation c is already in slope-intercept form with a slope of -5.
• Equation d can be rewritten as y = -x - 11 after distributing the negative sign, which has a slope of -1.

Comparing the slopes, none of these lines have the same slope and therefore none are parallel to each other.