A line’s slope-intercept form combines its rate of change with its value when the input is zero. On a graph, read the marked coordinates and the axis labels, then use Desmos to divide the altitude change by the time change. Put that slope and starting altitude into . Match both the rate and the starting value; a line can have one right and the other wrong.
Hints
- Hint 1
The y-intercept is where the line meets the vertical axis, so its -coordinate is . Read the marked point at time zero. What altitude did the drone have when it took off?
- Hint 2
A line’s slope is its change in altitude divided by its change in time. Use the marked coordinates, not the number of grid boxes. How much does each coordinate change between the two points?
- Hint 3
In , is the slope and is the altitude at time zero. Which equation matches both the rate you found and the starting altitude?
Step-by-step
Read the starting altitude and find the slope
Step 1Read the altitude at takeoff
The marked point means that at time zero, the drone is meters high. This is the y-intercept, where the line meets the vertical axis, so the starting value is .
- Step 2
Find the altitude gained each second
The other marked point is . The slope is the change in altitude divided by the change in time. Type in Desmos; it shows . So the drone gains meters per second. Use the coordinate values rather than counting boxes: the altitude axis increases by meters per tick.
- Step 3
Write the equation of the drone’s altitude
Use slope-intercept form , where is the slope and is the altitude at time zero. Put in both values:
The drone starts at meters and gains meters each second. Choice A.