Question

Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.

a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?

Answer 1

a. The coordinates of the first train are (-12,6), and those of the second train are (20, 35)

b. The slope is the x-axis distance divided by the y-axis distance, or $\frac{rise}{run}$.  Therefore, the slope is $\frac{6}{-12}$, or -0.5.  It is neither horizontal or vertical.  The line equation could be presented as the following:

Slope intercept: $y=-0.5x$
Standard: $y+0.5x=0$

c. Line equation: $y= -\frac{1}{3} x$