Answer:
(a) 11.6184
(b) 7.7664
(c) 9.9084
(d) y = 0.18x +9.1164
Explanation:
You want various function values and the equation for a relation with a constant rate of change of 0.18 and the value 10.11 when x = 5.52.
(d) Equation
Given a point on the relation and the rate of change, we can use the point-slope form of the equation for a line to find the desired equation.
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -10.11 = 0.18(x -5.52) . . . . . line with slope 0.18 thru point (5.52, 10.11)
y = 0.18x +9.1164 . . . . . . add 10.11 and simplify
The equation for y in terms of x is y = 0.18x +9.1164.
(a) x = 13.9
The calculator used for the attachment has been given the definition ...
Y0(x) = 0.18(x -5.52) +10.11 . . . . . . . point-slope equation for y
Using the simplified form of that formula we find
y = 0.18(13.9) +9.1164
y = 11.6184 for x = 13.9
(b) x = -7.5
The attached calculator output shows ...
y = 0.18(-7.5) +9.1164
y = 7.7664 for x = -7.5
(c) x = 4.4
The attached calculator output shows ...
y = 0.18(4.4) +9.1164
y = 9.9084 for x = 4.4
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Additional comment
"Rate of change" is another name for "slope". The rate of change of a linear function is the slope of the line on its graph, the ratio of "rise" to "run". For a linear function, the rate of change is a constant.
There are several useful forms of the equation for a line. One commonly used is the "slope-intercept form", y = mx +b, where m is the slope, and b is the y-intercept, the value of y when x=0.
The form useful when the slope and a point are given, as here, is shown above. It is
y -k = m(x -h) . . . . . . . . equation of line with slope m through point (h, k)
As above, this can be rearranged to give the slope-intercept form. This rearrangement is accomplished by the "ExpandAll" function in the attachment, which simplifies the function value 0.18(x-5.52)+10.11 to 0.18x+9.1164 for Y0(x).
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