Download 1-4 Writing Equations

Advanced Mathematical Concepts
Chapter 1
Lesson 1-4
Example 1
Write an equation in slope-intercept form for each line described.
2
a. a slope of - and a y-intercept of -5
3
2
Substitute -3 for m and -5 for b in the general slope-intercept form.
y  mx  b  y   2 x  5
3
The slope-intercept form of the equation of the line is y   2 x  5 .
3
b. a slope of 2 and passes through the point at (-2, 4).
Substitute the slope and coordinates of the point in the general slope-intercept form of a linear equation.
Then solve for b.
y  mx  b
4  2(2)  b
Substitute 4 for y, - 2 for x, and 2 for m.
8b
Add 4 to each side of the equation.
The y-intercept is 8. Thus, the equation for the line is y = 2x + 8.
Example 2
CONSUMER Suzanne O’Connell is planning to lease a new car. The total inception costs are $2350
and her monthly payment, thereafter, is $325. Write an equation that models the total expense y after x
months.
The initial cost is the y-intercept of the graph. Because the total expense rises $325 each month, the slope is
325.
y  mx  b
y  325 x  2350
Substitute 325 for m and 2350 for b.
The total expense can be modeled by y  325x  2350 .
Advanced Mathematical Concepts
Chapter 1
Example 3
POPULATION The age group consisting of individuals 65 years and older has been growing for the
last century. The table shows the annual percentages of the U.S. population that has been 65 years and
older since 1920.
Individuals 65 Years and Older
a. Find a linear equation that can be used as a model
Number of
Percent of U.S.
to predict what percent of the U.S. population is
Years Since
Population
65 years or older in any given year.
1920
0
4.7
b. Assume that the rate of growth of this age group
10
5.4
remains constant over time and use the equation
20
6.8
to predict the percent of the U.S. population that
30
8.1
will be 65 years and older in the year 2020.
40
9.2
50
9.8
c. Evaluate the prediction.
60
11.3
70
12.5
a. Graph the data. Then select two points to
represent the data set and draw a line that might
approximate the data. Suppose we choose (0,
4.7) and (70, 12.5). Use the coordinates of those
points to find the slope
of the line you drew.
y2 - y1
m = x2 - x1
12.5 - 4.7
= 70 - 0
0.11
x1 = 0, y1 = 4.7, x2 = 70, y2 = 12.5
Thus for each 1-year increase, the percent of the U.S. population
that is 65 years and older grows by 0.11 percent.
Use the point-slope form.
y - y1 = m(x - x1)
y - 4.7 = 0.11(x - 0)
Substitute 0 for x1, 4.7 for y1, and 0.11 for m.
y = 0.11x + 4.7
The slope-intercept form of the model equation is y = 0.11x + 4.7.
Advanced Mathematical Concepts
Chapter 1
b. Evaluate the equation for x = 2020 to predict the percent of the U.S. population that is
65 years and older in that year. The years since 1920 will be 2020 - 1920 or 100. So x = 100.
y = 0.11x + 4.7
y = 0.11(100) + 4.7
Substitute 100 for x.
y = 15.7
The predicted percent of the U.S. population that will be 65 years and older in the year 2020 is about
15.7%.
c. Most of the actual data points are close to the graph of the model equation. Thus, the equation and the
prediction are probably reliable.