NOTE In Example 7,the same result would be found by using for.
We could also substitute the slope and either given point in slope-intercept form
y=mx+band then solve for b, as in Example 5.
1 - 2, 5 2 1 x 1 , y 12
216 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
Equation Description Example
Vertical line
Slope is undefined.
x-intercept is
Horizontal line
Slope is 0.
y-intercept is
Slope-intercept form
Slope is m.
y-intercept is
Point-slope form
Slope is m.
Line passes through
Standard form
Slope is
x-intercept is
y-intercept is A0,
C
BB.
A
C
A^ , 0B.
-
A
B^.
AxByC 3 x- 2 y= 12
1 x 1 , y 12.
y+ 3 =
3
yy 1 m 1 xx 12 2 1 x- 22
1 0, b 2.
y=
3
ymxb 2 x- 6
1 0, k 2.
yk y= 3
1 k, 0 2.
xk x= 3
A summary of the forms of linear equations follows.
NOTE Slope-intercept form is an especially useful form for a linear equation
because of the information we can determine from it. It is also the form used by
graphing calculators and the one that describes a linear function.
Writing an Equation of a Line That Describes Data
The table lists the average annual cost (in dollars) of tuition
and fees for in-state students at public 4-year colleges and
universities for selected years. Year 1 represents 2001, year
3 represents 2003, and so on. Plot the data and write an
equation that approximates it.
Letting yrepresent the cost in year x, we plot the data
as shown in FIGURE 34on the next page.
EXAMPLE 8
Forms of Linear Equations
OBJECTIVE 5 Write an equation of a line that fits a data set.If a given set
of data fits a linear pattern—that is, if its graph consists of points lying close to a
straight line—we can write a linear equation that models the data.
Source:The College Board.
Year Cost (in dollars)
1 3766
3 4645
5 5491
7 6185
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