Question

3. Keenen gets on the train to ride around the park. As he is riding the train the conductorsays that they are going to build a train crossing ahead. He wants Keenen's help becausehe knows that the train tracks are on the equation 4x +2y 16 and that the crossing will bperpendicular to that equation passing through the point (8, 15). Help Keenen determinethe equation of the line that the train crossing will appear.

Answer 1

First, we need to get the slope of the equation of the train tracks. We can transform the given equation into the slope-intercept form.
4x +2y = 16
y = -2x +8

The slope of the equation is -2.

A perpendicular line will have the same slope but the opposite sign.
So, the slope of the line of the train crossing is 2. Since, it will pass through the point (8,15), the slope-intercept form can also be used to solve for the equation.
 y = mx + b

The slope is 2, so m=2. We solve b by substituting the coordinates.
15 = 2(8) +b
b = -11

The equation is now,
y = -2x - 11

Or it can also be expresses as:
2x - y = 11