For a linear function, two values at different inputs let you find the slope, or how much the output changes per input unit. Divide the output change by the matching input change; Desmos can handle the arithmetic. Then use that slope to work back to input . An output given at another input is not automatically .
Hints
- Hint 1
A function value pairs an input with its output: gives the point . Write the other input-output pair in the same order before finding how fast the line changes.
- Hint 2
The slope is the change in output divided by the change in input. Use the two points in the same order for both changes. Once you know the slope, how many input units must you move from to reach ?
Step-by-step
Find the slope, then work back to zero
Step 1Turn the function values into points
A function value tells you an input and its output. Since , the line passes through . Since , it also passes through . Keep each input with its output.
- Step 2
Find the change per input unit
The slope tells you how much the output changes when the input increases by . Divide the output change by the matching input change: type in Desmos. It shows , so each step to the right raises the output by .
- Step 3
Work back to input zero
From input to input is two steps left, so subtract the slope twice from . Type in Desmos; it shows . This is , the output at input , also called the -intercept. Choice D.