Transcript Forms of a linear equation Slope-intercept Form y = mx + b Standard Form Ax + By = C Point-Slope Form y – y1 =

Forms of a linear equation
Slope-intercept Form y = mx + b
Standard Form
Ax + By = C
Point-Slope Form
y – y1 = m(x – x1)
If given the slope and yintercept,
use slope-intercept form.
Example
m = 5, b = 7
5 x + ___
7
y = ___
(B8) Writing the Equation of a Line
Review of Slope-Intercept Form
The slope-intercept form of a linear equation is
y = mx + b.
m represents the slope
b represents the y-intercept
Review of Slope-Intercept Form
Name the slope and y-intercept of each equation:
y = -4x + 3
1
2
x
8x + y =
3

4
y=5–
4x - 2y =10
y=
1
3
y=5
x
m = -4, b =3
m=- 1 ,b=5
2
Rewrite as y = -8x

3
4
, m = -8, b =

3
4
Rewrite as y = 2x - 5, m = 2, b = -5
Rewrite as y =
1
3
x + 0, m =
1
3
,b=0
Rewrite as y = 0x + 5, m = 0, b = 5
Write the equation of a line given...
1. Slope and y-intercept
2. Graph
3. x - and y-intercepts
4. Slope and Point
Two Points
1. Find the Equation of the Line
Given the Slope and y-intercept
●Substitute m and b into y = mx + b
m = -3, b = 1
y = -3x + 1
m = -2, b = -4
y = -2x - 4
m = 0, b = 10
y = 0x + 10, y = 10
m = 1, b = 0
y = 1x + 0, y = x
m = 0, b = 0
y = 0x + 0, y = 0
2. Find the Equation of a Line
Given the Graph
• Find the y-intercept from the graph.
• Count the slope from the graph.
vertical change
rise change in y


horizontal change run change in x
• To write the equation of the line,
substitute the slope and y-intercept in the
slope-intercept form of the equation.
Example 1
● b = -3
3
2
●m=
●y=
3
2
+2
x-3
+3
y
x
Example 2
●b = 1
●m =
●y =
1

2
1

2
-2
+1
x+1
y
x
Example 3
●b = 4
● m = 0/1= 0
x
● y = 0x + 4, y = 4
y
3. Find the Equation of the Line
Given the x- and y - intercepts
● Write the intercepts as ordered pairs.
The x-intercept 4 is the ordered pair (4, 0).
The y-intercept -2 is the ordered pair (0, -2).
● Calculate the slope.
● Substitute the slope and the y-intercept (b) into
the slope-intercept formula.
Example
Write the equation of the line with x-intercept 3
and y-intercept 2.
x-intercept 3 = (3, 0); y-intercept 2 = (0, 2)
Slope:
y2  y1
m=
x2  x1
20
m
03
2 2
m

3 3
y = mx + b
2
y   x2
3
If
given
the
a
point
and
the
4. Find the Equation of the Line
slope,
Given the Slope and a Point
Use slope-intercept form.
Example
m = –2, contains (5, –8)
Step 1
Substitute –2 for m, 5 for x, and
–8 for y; then simplify to find
the value of b.
y = mx + b
–8 = –2(5) + b
–8 = –10 + b
2=b
Step 2
Substitute –2 for m, and 2 for b.
y = –2x + 2
5. Find the Equation of the Line
If given
Giventwo
Twopoints,
Points
First, find the slope using the slope formula.
Example
contains (5, –8) and (2, 7)
y2  y1
m
x2  x1
m
= 7 – -8
2–5
m = 15
–3
m = –5
If given two points,
Then use the slope and EITHER point to work
like the previous example.
y = mx + b
m = –5,
contains (5, –8) and (2, 7)
7 = -5(2) + b
7 = -10 + b
b = 17
y = –5x + 17
Example
● Write the equation of the line that goes
through the points (3, 2) and (5, 4).