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
119
likes593 views
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
4.7114 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.
Frequently asked questions (FAQs)
Question: What is the area under the curve of f(x) = 2x + 3 from x = 1 to x = 5 using the Fundamental Theorem of Calculus?
+
Math question: What is the limit as x approaches 2 of the function f(x) = (x^2 - 4) / (x - 2) ?
+
What is the angle in radians for the point on the unit circle corresponding to the coordinates (-1/2, sqrt(3)/2)?
+
New questions in Mathematics