Question

On September 5th, 1977, the Voyager 1 spacecraft was launched from Cape Canaveral, Florida to observe Jupiter and Saturn. Just like a pilot lands an aircraft, scientists carefully plotted the trajectory of the Voyager 1 spacecraft so that it could use the gravity of other planets to sling-shot it further and deeper into space! On November 20th, 1980, Voyager 1 had successfully completed its mission. However, due to excellent planning and precision of the scientists, Voyager is still out there today collecting data and traveling deeper and deeper into space!

Answer 1

Now it is your turn to plan the trajectories required to launch a spacecraft through a specific route in space. The launch area is identified on the map below. Select three points for your spacecraft to travel through and label them Point A, Point B, and Point C.

Answer 2

You must show your work on each question below.

Determine the equation of the line, in standard form, that will get your spacecraft from the Launch Area to Point A.

Determine the equation of the line, in point-slope form, that will get your spacecraft from Point A to Point B.

Determine the equation of the line, in slope-intercept form, that will get your spacecraft from Point B to Point C.

In question 2, you selected one of two points (Point A or Point B) to be included in your point-slope equation. Write the point-slope form of that equation again, using the other point’s coordinates.

Convert the equations you arrived at in question 2 and question 4 into slope-intercept form.

Does the point you select matter when your write a point-slope equation? Explain your reasoning using complete sentences.

Reflect back on this scenario and each equation you created. Would any restrictions apply to the domain and range of those equations? Explain your reasoning using complete sentences.

Explain, using complete sentences, why it is important to understand any limitations on the domain and range.