Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
A linear equation o line can be expressed in the form y = mx + b.
where
Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
In this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:
So, the slope m can be calculated as:
[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]
Solving:
m= -58
Considering point 1 and the slope m, you obtain:
11.5= -58×0.1 +b
11.5= -5.8 + b
11.5 + 5.8= b
17.3= b
Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
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