Answer:
see below
Step-by-step explanation:
You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).
Slope
The two-point equation for the slope of a line is ...
m = (y2 -y1)/(x2 -x1)
For the first pair of points, the slope is ...
m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3
The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.
Y-intercept
The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:
y = mx + b
b = y - mx
In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...
b = 5 -(-7/3)(-8) = -41/3
The other two y-intercepts are computed to be -13/3 and -20/7.
Slope-intercept function
The piecewise function that models the given data is ...
[tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]
__
Additional comment
There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.
The same repetitive computations are handled nicely by a spreadsheet.
<95141404393>
