Question 50335: I can not figure out how to exactly put this problem into an Linear equation, basically because i don't know where the numbers fit into the equation. So here is the problem.
The number of married couples in the United States in 1995 was 53.9 million. Im 2000, the number of married couples grew to 55.3 million. Write a linear equation that gives the number of married couples in terms of the year. Let x represent the year with x=5 corresponding to 1995.
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The number of married couples in the United States in 1995 was 53.9 million. Im 2000, the number of married couples grew to 55.3 million. Write a linear equation that gives the number of married couples in terms of the year. Let x represent the year with x=5 corresponding to 1995.
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You are given two points and asked to find the equation.
Points are (5,53.9) and (10,55.3)
You want y=mx+b and need to find m and b.
m=[55.3-53.9]/[10-5]
=1.4/5=0.28
Using (5,53.9)and m=0.28 you can solve for b as follows:
53.9=(0.28)(5)+b
b=52.5
EQUATION:
y=0.28x+52.5
Cheers,
Stan H.
Answer by tutorcecilia(2152)  (Show Source):
You can put this solution on YOUR website! The number of married couples in the United States in 1995 was 53.9 million. Im 2000, the number of married couples grew to 55.3 million. Write a linear equation that gives the number of married couples in terms of the year. Let x represent the year with x=5 corresponding to 1995.
A linear equation means that as one item independently increases, another item dependently increases.
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What is independently increasing in your problem? The years were independently increasing since "time" is not dependent on anything -- it keeps moving forward.
x = time = 1995, 1996, 1997, 1998 ....etc. Substitute numbers for the year. So, 1995 = 5
1996 = 6
1997 = 7, etc.
2000 = 10
.
What increased dependently upon time? The number of married couples.
y = 53.9 when x = 1995 = 5
Point: (5, 53.9)
.
y = 55.3 when x = 2000 = 10
Point: (10, 55.3)
.
Use the slope-intercept form as your formula for a line (or linear equation)]
y=mx+b [We need the slope(m) and the y-intercept (b)]
Slope = m = (y2-y1)/x2-x1)
Slope = m = (55.3-53.9)/10-5) [Plug-in the points.
Slope = m =1.4/5 = 0.28
.
y=mx+b
55.3=(.28)(10)+b [Plug-in the known values and solve for b]
55.3-2.8=2.8-2.8+b
52.5=b
y=.28x+52.5 [Plug-in the values for the slope (m) and the y-intercept (b)for the equation of the line]
.
To find out the number of married couples for any given year, just plug-in the year (x) and solve for the number of couples.
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