2.4 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.
2.
3.
4.
5.
Slope and y-intercept
Graph
Slope and one point
Two points
x - and y-intercepts
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 a Line
Given the Point and the Slope
● Use the Point-Slope Formula:
( y  y1 )  m( x  x1 )
● ( x1 , y1 ) is the given point
● Substitute m and ( x1 , y1 ) into the
formula
Example
● Write the equation of the line with slope = -2
and passing through the point (3, -5).
● Substitute m and ( x1 , y1 ) into the Point-Slope
Formula.
( y  y1 )  m( x  x1 )
( y  5)  2( x  3)
y  5  2 x  6
y  2 x  1
4. Find the Equation of the Line
Given Two Points
● Calculate the slope of the two points.
y2  y1
m=
x2  x1
● Use one of the points and the slope to
substitute into the Point-Slope formula.
( y  y1 )  m( x  x1 )
Example
● Write the equation of the line that goes
through the points (3, 2) and (5, 4).
y2  y1
m=
x2  x1
42
m
53
2
m  1
2
( y  y1 )  m( x  x1 )
( y  2)  1( x  3)
y2 x3
y  x 1
5. 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