Expert: Richard J. Raridon - 7/9/2006

Question
Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-intercept form of the equation, and graph the function. Give the domain and range as defined by the points, and also the domain and range of the entire function.

What is the Equation in Slope-Intercept Form:  
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Followup To

Question -
In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.

Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph you have drawn, and also the domain and range of the entire function excluding unrealistic values.

Graph:


Graph Type:

Explanation:

Domain:

Range:


3) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.
a) Write a linear function that expresses the distance traveled, d, as a function of time, t.
Answer:




b) How far have you traveled after 4 hours?
Answer:



c) Write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t.
Answer:



d) How far will I need to travel to reach San Francisco after I have traveled 3 hours?
Answer:








Answer -
1) Let I = income and n = no. of $0.25 increases
I = (800-40n)(2.25+0.25n) = 1800+110n-10n^2
This is a parabola which you can plot by putting in a few values for n and calculating I.  n can have values from 0 to 19.  
3) a) d = 60t
b) d = 60(4) =
c) s = 60t
d) it takes a total of 8 hours to get there

Answer
the standard equation for a line is y = mx+b, where m is the slope and b is the y-intercept.
since it only takes two points to determine a line you don't need all three points.  pick any two.  For example,
4 = m(1)+b and 7 = m(2)+b
so m=3, b=1 and your equation is y = 3x+1
you can graph it since you already have the points.
the range defined by the points is 4 =< y =< 10 and
1 =< x =< 3.  
for the entire function the range is infinity.
they didn't have domains when I took algebra