A set of train tracks are modeled by 3x+4y=-36 and a road is modeled by y=-3/4x + 11. Will the road cross the train tracks? Explain the reasoning

1. Convert the train tracks equation to slope-intercept form (y = mx + b):

3x + 4y = -36

Subtract \(3x\) from both sides:

4y = -3x - 36

Divide every term by \(4\):

y = -\frac{3}{4}x - 9

The slope (m) of the train tracks is -3/4.

2. The road is already in slope-intercept form:

y = -\frac{3}{4}x + 11

The slope (m) of the road is -3/4

3. Compare the slopes:

Both lines have the same slope but different y-intercepts -9 and 11.

4. Since they have the same slope but different y-intercepts, the lines are parallel and will not intersect.

The road and train tracks are parallel, hence they do not cross each other.