Can you help me solve this

Question

A section of a biking trail begins at the coordinates (-3,14) and follows a straight path that ends at the coordinates (6,-1). What is the rate of change of the biking trail ?

Answer 1

Hello Lauryn. In order to solve this problem, you will need to know the rate of change formula (or formula for slope,m) is:

m= (y₂-y₁)/₍x₂-x₁₎

We know that x1=-3, x2=6, y1= 14, and y2= -1 because all of these values are provided in the problem. We can now plug our x and y values into the rate of change formula and solve for m. Doing so yields:

m=(y₂-y₁)/(x₂-x₁)

m=(-1-14)/(6-(-3))

Two negative signs become a positive (+) sign, so we now have:

m=(-1-14)/(6+3) = -15/9

-15/9 can be further reduced to -5/3 by dividing the numerator and denominator by the least common multiple of 15 and 9, which is 3.

Thus, the final answer is -5/3.

I hope that this guided answer has helped you in understanding how to use the rate of change (or slope) formula to solve a problem.