Final answer:
The calculator is displaying the value of a linear function. By finding the equation of the line through the given points (8, 6) and (12, 9), we can determine the function. The equation of the linear function is y = (3/4)x.
Step-by-step explanation:
The calculator is displaying the value of a linear function when certain numbers are entered. We can determine the function by finding the equation of the line that passes through the given points. Using the coordinates (8, 6) and (12, 9), we can find the slope of the line:
slope = (y2 - y1) / (x2 - x1) = (9 - 6) / (12 - 8) = 3 / 4
Now we can use the slope-intercept form of a linear equation to find the equation of the line:
y = mx + b, where m is the slope and b is the y-intercept.
Using the point-slope form of an equation with the slope (3/4) and the coordinates (8, 6), we can solve for b:
6 = (3/4)(8) + b
6 = 6 + b
b = 0
Therefore, the equation of the linear function is y = (3/4)x. When any number n is entered, the calculator will display the value (3/4)n.