For the demand equation below, $x$ represents the quantity demanded in units of 1000 and $p$ is the unit price in dollars.
\[
2 x+4 p-32=0 ; p=2
\]
(a) Sketch the demand curve. (Sketch the curve as a segment.)
Answer
The demand curve can be represented by the equation \(x = -2p + 16\). To sketch the curve as a segment, plot the points \((x, p)\) for different values of \(p\) and connect them with a line. The curve will be a straight line with a slope of -2 and a y-intercept of 16.
Step 1 ：Given the demand equation: \(2x + 4p - 32 = 0\) and \(p = 2\)
Step 2 ：Find the value of \(x\) when \(p = 2\):
Step 3 ：\(2x + 4(2) - 32 = 0\)
Step 4 ：\(2x + 8 - 32 = 0\)
Step 5 ：\(2x = 24\)
Step 6 ：\(x = 12\)
Step 7 ：Find the general equation for \(x\) in terms of \(p\):
Step 8 ：\(2x + 4p - 32 = 0\)
Step 9 ：\(2x = -4p + 32\)
Step 10 ：\(x = -2p + 16\)
Step 11 ：The demand curve can be represented by the equation \(x = -2p + 16\). To sketch the curve as a segment, plot the points \((x, p)\) for different values of \(p\) and connect them with a line. The curve will be a straight line with a slope of -2 and a y-intercept of 16.
