2.
Various Forms of an Equation of a
Line.
SlopeIntercept Form
Standard Form
PointSlope Form
slope of the line
intercept
y mx b
m
b y
= +
=
= −
, , and are integers
0, must be postive
Ax By C
A B C
A A
+ =
>
( )
( )
1 1
1 1
slope of the line
, is any point
y y m x x
m
x y
− = +
=


3.
KEY CONCEPT
Writing an Equation of a Line
– Given slope m and yintercept b
• Use slopeintercept form y=mx+b
– Given slope m and a point (x1,y1)
• Use pointslope form
– y  y1 = m ( x – x1)
• Given points (x1,y1) and (x2,y2)
– Find your slope then use pointslope form with either point.
4.
Write an equation given the slope and yinterceptEXAMPLE 1
Write an equation of the line shown.
5.
SOLUTION
Write an equation given the slope and yinterceptEXAMPLE 1
From the graph, you can see that the slope is m =
and the yintercept is b = –2. Use slopeintercept form
to write an equation of the line.
3
4
y = mx + b Use slopeintercept form.
y = x + (–2)
3
4
Substitute for m and –2 for b.
3
4
y = x –2
3
4
Simplify.
6.
GUIDED PRACTICE for Example 1
Write an equation of the line that has the given slope
and yintercept.
1. m = 3, b = 1
y = x + 13
ANSWER
2. m = –2 , b = –4
y = –2x – 4
ANSWER
3. m = – , b =3
4
7
2
y = – x +3
4
7
2
ANSWER
7.
Write an equation given the slope and a pointEXAMPLE 2
Write an equation of the line that passes
through (5, 4) and has a slope of –3.
Because you know the slope and a point on the
line, use pointslope form to write an equation of
the line. Let (x1, y1) = (5, 4) and m = –3.
y – y1 = m(x – x1) Use pointslope form.
y – 4 = –3(x – 5) Substitute for m, x1, and y1.
y – 4 = –3x + 15 Distributive property
SOLUTION
y = –3x + 19 Write in slopeintercept form.
8.
EXAMPLE 3
Write an equation of the line that passes through (–2,3)
and is (a) parallel to, and (b) perpendicular to, the line
y = –4x + 1.
SOLUTION
a. The given line has a slope of m1 = –4. So, a line
parallel to it has a slope of m2 = m1 = –4. You know
the slope and a point on the line, so use the point
slope form with (x1, y1) = (–2, 3) to write an equation
of the line.
Write equations of parallel or perpendicular lines
9.
EXAMPLE 3
y – 3 = –4(x – (–2))
y – y1 = m2(x – x1) Use pointslope form.
Substitute for m2, x1, and y1.
y – 3 = –4(x + 2) Simplify.
y – 3 = –4x – 8 Distributive property
y = –4x – 5 Write in slopeintercept form.
Write equations of parallel or perpendicular lines
10.
EXAMPLE 3
b. A line perpendicular to a line with slope m1 = –4 has
a slope of m2 = – = . Use pointslope form with
(x1, y1) = (–2, 3)
1
4
1
m1
y – y1 = m2(x – x1) Use pointslope form.
y – 3 = (x – (–2))
1
4
Substitute for m2, x1, and y1.
y – 3 = (x +2)
1
4
Simplify.
y – 3 = x +
1
4
1
2
Distributive property
Write in slopeintercept form.
Write equations of parallel or perpendicular lines
1 7
4 2
y x= +
11.
GUIDED PRACTICE for Examples 2 and 3GUIDED PRACTICE
4. Write an equation of the line that passes through
(–1, 6) and has a slope of 4.
y = 4x + 10
5. Write an equation of the line that passes through
(4, –2) and is (a) parallel to, and (b) perpendicular
to, the line y = 3x – 1.
y = 3x – 14ANSWER
ANSWER
12.
Write an equation given two pointsEXAMPLE 4
Write an equation of the line that passes
through (5, –2) and (2, 10).
SOLUTION
The line passes through (x1, y1) = (5,–2) and
(x2, y2) = (2, 10). Find its slope.
y2 – y1
m =
x2 – x1
10 – (–2)
=
2 – 5
12
–3
= = –4
13.
Write an equation given two pointsEXAMPLE 4
You know the slope and a point on the line, so use
pointslope form with either given point to write an
equation of the line. Choose (x1, y1) = (2, 10).
y2 – y1 = m(x – x1) Use pointslope form.
y – 10 = – 4(x – 2) Substitute for m, x1, and y1.
y – 10 = – 4x + 8 Distributive property
Write in slopeintercept form.y = – 4x + 8
Be the first to comment