(b)Through with slope
Point-slope formLetDistributive propertyAdd to each side.Combine like terms. NOW TRYOBJECTIVE 4 Write an equation of a line by using two points on the line.
Many of the linear equations in Sections 3.1–3.3were given in the form
Standard formcalled standard form, where A, B, and C are real numbers and Aand Bare not both 0.
In most cases, A, B, and Care rational numbers. For consistency in this book, we give
answers so that A, B, and Care integers with greatest common factor 1 and.
NOTE The definition of standard form is not the same in all texts. A linear equation
can be written in many different, equally correct, ways. For example,
all represent the same set of ordered pairs. When giving answers in standard form, let
us agree that is preferable to the other forms because the greatest
common factor of 3, 4, and 12 is 1 and.
Writing the Equation of a Line by Using Two PointsWrite an equation of the line through the points and Give the final
answer in slope-intercept form and then in standard form.
First, find the slope of the line, using the slope formula.
Now use either or and either slope-intercept or point-slope form.
We choose and
point-slope form.LetDistributive propertyAdd to each side.Slope-intercept form Combine like terms.Multiply by 5 to clear fractions.Standard form x+ 5 y= 23 Add x. NOW TRY
5 y=-x+ 23
y=-
1
5
x+
23
5
y=- 4 =^205
1
5
x+
3
5
+
20
5
y- 4 =-
1
5
x+
3
5
y - 4 = - y 1 =4,m=- 15 ,x 1 =3.
1
5
1 x- 32
1 3, 4 2y- y 1 = m 1 x- x 12
1 - 2, 5 2 1 3, 4 2
slope m=
y 2 - y 1
x 2 - x 1
=
5 - 4
- 2 - 3
=
1
- 5
= -
1
5
1 - 2, 5 2 1 3, 4 2.
EXAMPLE 7
AÚ 0
3 x+ 4 y= 12
3 x+ 4 y= 12, 6 x+ 8 y=24, and - 9 x- 12 y=- 36
AÚ 0
AxByC,
y=
3
5
x-
2
5
y=
3
5
x-
12
5
+
10
5
y- 2 =
3
5
x-
12
5
y - 2 = y 1 =2, m=^35 , x 1 =4.
3
5
1 x- 42
y-y 1 =m 1 x-x 12
31 4, 2 2 , 5
SECTION 3.4 Writing and Graphing Equations of Lines 215
NOW TRY
EXERCISE 7
Write an equation of the line
through the points
and. Give the final
answer in
(a)slope-intercept form and
(b)standard form.
1 6, - 22
1 4, 1 2
NOW TRY ANSWERS
6.
- (a)
(b) 3 x+ 2 y= 14
y=-^32 x+ 7y=-^25 x+^15NOW TRY
EXERCISE 6
Write an equation of the line
through , with slope
Give the final answer in
slope-intercept form.