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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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Answer:
Part 1) Subtraction Property of Equality
Part 2) This property can be used , because addition and subtraction have inverse relationships
Step-by-step explanation:
we know that
The<u><em> subtraction property of equality</em></u> tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same
so
we have
Solve for y
Applying Subtraction Property of Equality
subtract 10.50 both sides
Remember that this property can be used , because addition and subtraction have inverse relationships.