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

y = -4x + 3

y = 5 – x

8x + y =

4x - 2y =10

y = x

y = 5

1

2

Name the slope and y-intercept of each equation:

1

2

3

4

3

4

3

4

1

3

1

3

1

3

m = -4, b =3

m = - , b = 5

Rewrite as y = -8x , m = -8, b =

Rewrite as y = 2x - 5, m = 2, b = -5

Rewrite as y = x + 0, m = , 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. Slope and one point

4. Two points

5. x - and y-intercepts

1. Find the Equation of the LineGiven the Slope and y-intercept

m = -3, b = 1

m = -2, b = -4

m = 0, b = 10

m = 1, b = 0

m = 0, b = 0

●Substitute m and b into y = mx + b

y = -3x + 1

y = -2x - 4

y = 0x + 10, y = 10

y = 1x + 0, y = x

y = 0x + 0, y = 0

2. Find the Equation of a LineGiven the Graph

• Find the y-intercept from the graph.• Count the slope from the graph.

• To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.

vertical change rise change in yhorizontal change run change in x

Example 1

●b = -3

●m =

●y = x - 3

3

2

x

y

+2

+33

2

Example 2

●b = 1

●m =

●y = x + 1

1

2

x

y

+1-2

1

2

Example 3

●b = 4

●m = 0/1= 0

●y = 0x + 4, y = 4

x

y

3. Find the Equation of a LineGiven the Point and the Slope

●Use the Point-Slope Formula:

● is the given point ●Substitute m and into the

formula1 1( , )x y

1 1( ) ( )y y m x x

1 1( , )x y

Example

●Write the equation of the line with slope = -2 and passing through the point (3, -5).

●Substitute m and into the Point-Slope Formula.

1 1( , )x y

1 1

5 2

( ) ( )

( ) ( )

5 2 6

3

2 1

y y m x x

y x

y x

y x

4. Find the Equation of the LineGiven Two Points

●Calculate the slope of the two points.

●Use one of the points and the slope to substitute into the Point-Slope formula.

1

2 1

2=y y

mx x

1 1( ) ( )y y m x x

Example

●Write the equation of the line that goes through the points (3, 2) and (5, 4).

1

2 1

4 2

5 32

12

2=y y

mx x

m

m

1 1( ) ( )

( 2) 1( 3)

2 3

1

y y m x x

y x

y x

y x

5. Find the Equation of the LineGiven 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: 1

2 1

2 0

0 32 2

3 3

2=y y

mx x

m

m

y = mx + b

22

3y x