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)
What is the sine of an angle in a right triangle if the length of the side opposite the angle is 5, and the length of the hypotenuse is 13?
+
What is the measure of angle x in a circle with a central angle of 120°?
+
What is the sine value of an angle, given the opposite side length is 8 and the hypotenuse is 10?
+
New questions in Mathematics