1. Find the equation of the line which passes through the point (-1,3) and is perpendicular to the line of equation x+2y=1.
Solution. First find the slope of the line x+2y=1. For this you write this equation in the form y = (-1/2)x+(1/2), so the slope is -1/2. The slope of a line perpendicular to x+2y=1 is the negative inverse of the slope, hence 2. The slope and one point completely determine the line. It has the general expression y=mx+b. Thus y=2x+b. To find b, impose the condition that it passes thru (-1,3), that is 3 = 2(-1)+b, so that b=5. The equation is y=2x+5.
2. Since the founding of the Equal Employment Opportunity Commission and the passage of equal pay laws, the gulf between men's and woman's earnings has continued to close gradually. At the beginning of 1990, women's wages were 68% of men's wages. At the beginning of the year 2000, women's wages were 80% of men's wages. If this gap continues to narrow linearly, what percentage of men's wages can we expect women's wages to be at the beginning of the year 2002?
Solution. The gulf percentage is a linear function of time, that is, its graph as a function of time is a line. Draw a coordinate system in which the x-axis represents time and the y-axis represents the gap percentage. At the beginning of 1990, the gulf was 68%. On the year 2000 the gulf was 80%. Thus this line is that which passes thru the points (1990,68) and (2000,80). The slope of this line is
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3. Let f be the function defined by f(x)=2x2+x-3.
(b) The values of f(x) at those points x are
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(c) Plot the points and join them with a line.
4. Does the point (-3, -1/13) lie in the graph of the function
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Solution. The point (a,b) is in the graph of f if and only if b=f(a). Thus we need to check whether f(-3) equals -1/13. Doing the calculation
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5. Sketch the graph of the function
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