Question

55. TECHNOLOGY

Answer 1

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.

Linear equation o line

A linear equation o line can be expressed in the form y = mx + b.

where

• x and y are coordinates of a point.
• m is the slope.
• b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

$m=\frac{y2-y1}{x2-x1}$

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.

Equation for the function in this case

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:

• (x1, y1)= (0.1, 11.5)
• (x2, y2)= (0.4, -5.9)

So, the slope m can be calculated as:

$m=\frac{-5.9-11.5}{0.4-0.1}$

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.

Learn more about the equation of a line having 2 points:

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