To determine if the graphs of the given lines are parallel, we need to check their slopes. Two lines are parallel if they have the same slope.
-
The first line is already in slope-intercept form \(y = mx + b\): \[ y = 6x + 9 \] From this, we see that the slope \(m\) is 6.
-
Now, we will reformat the second line, given by the equation: \[ 27x - 3y = -81 \] First, we can isolate \(y\) to put it into slope-intercept form. Start by moving \(27x\) to the other side: \[ -3y = -27x - 81 \] Next, divide through by -3 to solve for \(y\): \[ y = 9x + 27 \] From this equation, we see that the slope \(m\) of the second line is 9.
Now we can compare the slopes of both lines:
- Slope of the first line = 6
- Slope of the second line = 9
Since the slopes are different (6 ≠ 9), the lines are not parallel.
2 answers