1) The document discusses various forms of equations for lines, including slope-intercept form, standard form, and point-slope form. It provides definitions and examples of writing equations of lines given the slope and y-intercept or given two points on the line. 2) Key concepts covered include writing the equation of a line given its slope m and y-intercept b using slope-intercept form y=mx+b, or given slope m and a point (x1,y1) using point-slope form y-y1=m(x-x1). 3) Examples are provided for writing equations of lines using slope-intercept form when given slope and y-intercept, and using point-

1. Writing
Equations of a
Line

2. Various Forms of an Equation of a
Line.
Slope-Intercept Form
Standard Form
Point-Slope 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 y-intercept b
• Use slope-intercept form y=mx+b
– Given slope m and a point (x1,y1)
• Use point-slope form
– y - y1 = m ( x – x1)
• Given points (x1,y1) and (x2,y2)
– Find your slope then use point-slope form with either point.

4. Write an equation given the slope and y-interceptEXAMPLE 1
Write an equation of the line shown.

5. SOLUTION
Write an equation given the slope and y-interceptEXAMPLE 1
From the graph, you can see that the slope is m =
and the y-intercept is b = –2. Use slope-intercept form
to write an equation of the line.
3
4
y = mx + b Use slope-intercept 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 y-intercept.
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 point-slope form to write an equation of
the line. Let (x1, y1) = (5, 4) and m = –3.
y – y1 = m(x – x1) Use point-slope form.
y – 4 = –3(x – 5) Substitute for m, x1, and y1.
y – 4 = –3x + 15 Distributive property
SOLUTION
y = –3x + 19 Write in slope-intercept 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 point-slope form.
Substitute for m2, x1, and y1.
y – 3 = –4(x + 2) Simplify.
y – 3 = –4x – 8 Distributive property
y = –4x – 5 Write in slope-intercept 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 point-slope form with
(x1, y1) = (–2, 3)
1
4
1
m1
y – y1 = m2(x – x1) Use point-slope 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 slope-intercept 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
point-slope form with either given point to write an
equation of the line. Choose (x1, y1) = (2, 10).
y2 – y1 = m(x – x1) Use point-slope form.
y – 10 = – 4(x – 2) Substitute for m, x1, and y1.
y – 10 = – 4x + 8 Distributive property
Write in slope-intercept form.y = – 4x + 8