a table of values of a linear function is shown below. find the output when the input is n. type your answer…

Explanation:

Step1: Find the slope of the linear function

The slope (m) of a linear function (y = mx + b) can be found using the formula (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(1,7)) and ((x_2,y_2)=(2,10)). Then (m=\frac{10 - 7}{2 - 1}=3).

Step2: Find the (y -)intercept of the linear function

Use the point - slope form (y - y_1=m(x - x_1)). Substitute (m = 3) and ((x_1,y_1)=(1,7)). (y-7=3(x - 1)), expand to get (y-7=3x-3), then (y = 3x+4).

Step3: Find the output when input is (n)

Substitute (x = n) into the function (y = 3x + 4). The output is (3n+4).

Answer:

(3n + 4)