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Are the graphs of the lines in the pair parallel? Explain.

y = 4x – 4
24x – 4y = 96

Yes, since the slopes are the same and the y-intercepts are different.

No, since the y-intercepts are different.

Yes, since the slopes are the same and the y-intercepts are the same.

No, since the slopes are different.

1 answer

To determine whether the graphs of the given lines are parallel, we need to find their slopes.

  1. The first line is given in slope-intercept form: \[ y = 4x - 4 \] Here, the slope (m) is 4.

  2. The second line is given in standard form: \[ 24x - 4y = 96 \] We can convert it to slope-intercept form (y = mx + b) by solving for y:

    \[ -4y = -24x + 96 \] Dividing each term by -4: \[ y = 6x - 24 \] Here, the slope is 6.

Next, we compare the slopes of the two lines:

  • The first line has a slope of 4.
  • The second line has a slope of 6.

Since the slopes (4 and 6) are different, the lines are not parallel.

Thus, the correct answer is: No, since the slopes are different.