Question

Part A: A highway's path can be found using the equation 2x - 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely.

Part B: A turnpike's route is determined by the equation
y = 1/3x^2 . Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work.

Answer 1

Explanation:

Part A

2x-3y =21 in slope-intercept form is y=2/3x-7 one you graph the equation it would be a parallel to the equation shown above so there are no intersections

PART B

y=1/3x^2 and y= 2/3x - 5

1/3x^2 = 2/3x-5

1/3x^2=2/3x-5

then u multiply everything by 3

1/3x^2*3 =2/3x *3-5*3

the three for 1/3*3 cancels out so you are left with

1x^2= 2x -15

1x^2-2x+15=0

You can not factor it and well i guess there is no intersection

im sorry if i got this wrong bc i had a similar question just different numbers and i tried to solve this one the way i sloved mine so im not sure of my answer for part b