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Chapter 1: Problem 8
Find the slope of the line that passes through the given pair of points. $$ (-2,-2) \text { and }(4,-4) $$
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For each demand equation, where \(x\) represents the quantity demanded in units of 1000 and \(p\) is the unit price in dollars, (a) sketch the demand curve and (b) determine the quantity demanded corresponding to the given unit price \(p\). $$ p=-3 x+60 ; p=30 $$
Show that two distinct lines with equations \(a_{1} x+b_{1} y+\) \(c_{1}=0\) and \(a_{2} x+b_{2} y+c_{2}=0\), respectively, are parallel if and only if \(a_{1} b_{2}-b_{1} a_{2}=0\). Hint: Write each equation in the slope-intercept form and compare.
For wages less than the maximum taxable wage base, Social Security contributions by employees are \(7.65 \%\) of the employee's wages. a. Find an equation that expresses the relationship between the wages earned \((x)\) and the Social Security taxes paid \((y)\) by an employee who earns less than the maximum taxable wage base. b. For each additional dollar that an employee earns, by how much is his or her Social Security contribution increased? (Assume that the employee's wages are less than the maximum taxable wage base.) c. What Social Security contributions will an employee who earns \(\$ 65,000\) (which is less than the maximum taxable wage base) be required to make?
$$ \begin{array}{l} \text { The point }(-1,1) \text { lies on the line with equation } 3 x+\\\ 7 y=5 \end{array} $$
Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ x+2 y-4=0 $$
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