Answer:
[tex] f(x) = 7x + 5 [/tex].
Step-by-step explanation:
The equation that represents the function can be written in the slope-intercept form, [tex] f(x) = mx + b [/tex].
To create an equation, we need to find the slope (m) and the y-intercept (b) of the function.
First, calculate the slope of the function using two points, (1, 12) and (2, 19).
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19 - 12}{2 - 1} = \frac{7}{1} = 7 [/tex]
Next, find b by substituting x = 1, f(x) = 12, and m = 7 into [tex] f(x) = mx + b [/tex].
[tex] 12 = (7)(1) + b [/tex]
[tex] 12 = 7 + b [/tex]
Subtract 7 from each side
[tex] 12 - 7 = b [/tex]
[tex] 5 = b [/tex]
[tex] b = 5 [/tex]
Substitute m = 7 and b = 5 into [tex] f(x) = mx + b [/tex].
✅Thus, the equation that represents the function would be:
[tex] f(x) = 7x + 5 [/tex].
