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Sagot :
In order to find the equation relating the unit price p and the quantity x, let's use the slope-intercept form of the linear equation:
[tex]p=mx+b[/tex]Where m is the slope and b is the y-intercept.
To find the value of m and b, let's use the ordered pairs (x, p) given in the question.
The given points are (1600, 370) and (5600, 420), so we have:
[tex]\begin{gathered} (1600,370)\colon \\ 370=1600m+b \\ (5600,420)\colon \\ 420=5600m+b \end{gathered}[/tex]Subtracting the first equation from the second one, we have:
[tex]\begin{gathered} 420-370=5600m+b-(1600m+b) \\ 50=4000m \\ m=0.0125 \\ \\ 370=1600\cdot0.0125+b \\ b+20=370 \\ b=350 \end{gathered}[/tex]Therefore the equation is p = 0.0125x + 350.
For a unit price of $470, we have:
[tex]\begin{gathered} 470=0.0125x+350 \\ 0.0125x=120 \\ x=9600 \end{gathered}[/tex]The lowest price is given by x = 1 (at least one refrigerator will be marketed), so:
[tex]\begin{gathered} p=0.0125\cdot1+350 \\ p=350.01 \end{gathered}[/tex]
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