Question

Are the graphs of the lines in the pair parallel? Explain. y = 6x + 9 27x – 3y = –81 No, since the y-intercepts are different. Yes, since the slopes are the same and the y-intercepts are different. No, since the slopes are different. Yes, since the slopes are the same and the y-intercepts are the same.

Answer 1

No, since the slopes are different

Explanation:

Parallel lines by definition have the same slope but different y-intercepts. The slope of the line y = 6x + 9 is 6, the coefficient of x since the equation is given in slope-intercept form. Its y-intercept is 9.

For the second equation, 27x – 3y = –81 , we have to solve for y or re-write the equation in slope-intercept form;

-3y = -27x - 81

y = 9x + 27

The slope of this line is thus 9, the coefficient of x since the equation is in slope-intercept form. Its y-intercept is 27.

The two equations have different slopes and thus they are not parallel