Question
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
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Answer to a math question 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
Dexter
4.7113 Answers
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.
Subtract \(3x\) from both sides:
Divide every term by \(4\):
The slope (m) of the train tracks is -3/4.
2. The road is already in slope-intercept form:
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.
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