Answer:
- f(x) = x -5
- f(x) = -4
- f(x) = -5/3x +18
Step-by-step explanation:
You want the linear function that corresponds to the given pairs of points.
Slope
The slope can be found from ...
m = (y2 -y1)/(x2 -x1) . . . . . . . . . given f(x1) = y1, f(x2) = y2
For example, ...
m = (-3 -5)/(2 -10) = -8/-8 = 1
Intercept
The y-intercept can be found from ...
b = y -mx . . . . . . . . given m from above and f(x) = y
For example, ...
b = 5 -1(10) = -5
This tells you the equation for (1) f(10) = 5, f(2) = -3 is y = x -5.
Repetition
When working problems identical in nature, but with different numbers, it is convenient to use a calculator or spreadsheet to carry out the repetitive arithmetic. In the attachment, we have used a calculator to solve the three instance of the equations ...
m(x1) +b = (y1)
m(x2) +b = (y2)
The result tells us the linear functions are ...
- f(x) = x -5
- f(x) = -4
- f(x) = -5/3x +18
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Additional comment
The result matrix has pairs of values m, b in the rightmost column.
