A linear function has a constant slope: its output changes by the same amount for each one-unit increase in input. When you know the slope and one function value, find the change from the known input to the requested input. Multiply that change by the slope, then add it to the known output. Don’t mistake the known output for the value at input .
Hints
- Hint 1
In , is the input and is the output. Treat the given function value as a starting point: which input produces its known output?
- Hint 2
The slope tells you how much the output changes for each one-unit increase in input. Find the input change by subtracting the starting input from the requested input, including its negative sign.
- Hint 3
Start with the known output, then add the slope times the input change. Since the slope is negative and the input increases, should the new output be higher or lower?
Step-by-step
Use the slope to find the output change
Step 1Identify the known input and output
means input produces output , so the known point is . The belongs to input , not input .
- Step 2
Relate the two outputs using the slope
The slope means the output falls by for each one-unit increase in input. For a line, output change equals slope times input change. Subtract the starting input, , from the requested input, :
Subtracting a negative adds, so the input increases by .
- Step 3
Isolate the requested output
Add to both sides to get by itself:
- Step 4
Calculate the function value
Type in Desmos. It prints , so the value of is . Choice B.