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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.
<h3>Linear equation o line</h3>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:
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.
<h3>Equation for the function in this case</h3>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:
Solving:
<u><em>m= -58</em></u>
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
<u><em>17.3= b</em></u>
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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