Two values of a linear function give you two points on its line. Divide the change in output by the change in input to find the slope; Desmos can evaluate that fraction. Then use either point to find the intercept, the output when the input is . Watch the signs when subtracting and when solving for the intercept.
Hints
- Hint 1
A function value such as means input gives output . That gives you the point on the line. What point comes from the other function value?
- Hint 2
The slope is the output change divided by the input change. Subtract the outputs in the same order as their matching inputs. What sign should the slope have when the output falls as the input rises?
- Hint 3
In , the intercept is the output when . Neither given input is , so use one of the points to find after you find the slope.
Step-by-step
Find the slope, then the intercept
Step 1Turn the function values into points
means input gives output , so the line passes through . Likewise, gives the point . The output falls as the input rises, so expect a negative slope.
- Step 2
Find the slope
The slope is the output change divided by the input change. Subtract in the same order on top and bottom: . Type in Desmos. It displays , so the output drops by whenever the input rises by .
- Step 3
Find the intercept and write the rule
A linear rule has the form , where the intercept is the output at input . Use and the point : . Type ; tells Desmos to find . Under PARAMETERS, it shows . The given output isn't the intercept because its input is , not . So the rule is . Choice D.