Question 106·Easy·Systems of Two Linear Equations in Two Variables
The graph shows two lines, and , where represents time (in seconds) and represents the height (in meters) of two drones flying at constant speeds.
At what time will the two drones be at the same height?
For systems shown as two lines, the solution is their intersection. If the question asks “when” something is equal, look for the intersection and use the -coordinate; if it asks “what value,” use the appropriate coordinate ( or ) based on what the variables represent.
Hints
What does “same height” mean on the graph?
It means both drones have the same -value at the same -value, which happens where the two lines cross.
Locate the key point
Find the intersection point of the two lines on the coordinate grid.
Use the correct coordinate
The question asks for time, so use the -coordinate of the intersection point.
Desmos Guide
Enter the two lines
In Desmos, enter the equations and .
Find the intersection point
Click the intersection point of the two lines to display its coordinates .
Answer using the time coordinate
Use the -coordinate of the intersection as the time, so the answer is .
Step-by-step Explanation
Identify when the heights are equal
The two drones have the same height when their height-time graphs intersect (the point where the two lines cross).
Read the intersection and answer
From the graph, the lines intersect at . The time is the -coordinate, so the drones are at the same height at seconds.