1. 2.4 Writing Equations of Lines
Objectives:
● I will write linear equations given
the slope (m) and the y-intercept
(b).
● I will write linear equations given
the slope (m) and a point (x 1 , y 1 ).
● I will write linear equations given
two points (x 1 , y 1 ) and (x 2 , y 2 ).

2. 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

3. Review of Slope-Intercept Form
Name the slope and y-intercept of each equation :
y = -4x + 3 m = -4, b =3
1 1
y=5– x m=- ,b=5
2 2
3 3
8x + y = −
3 Rewrite as y = -8x − , m = -8, b = −
4 4 4
4x - 2y =10 Rewrite as y = 2x - 5, m = 2, b = -5
1 1 1
y= x Rewrite as y = 3
x + 0, m = 3
,b=0
3
y=5 Rewrite as y = 0x + 5, m = 0, b = 5

4. 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

5. 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

6. 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.

7. Example 1
● b = -3
3
● m=
2
+2 x
3
● y= 2
x-3 +3
y

8. Example 2
● b=1
1
● m= −
2 -2
+1
x
1
● y= −
2 x+1
y

9. Example 3
● b=4
● m = 0/1= 0 x
● y = 0x + 4, y = 4
y

10. 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

11. 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

12. 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 )

13. Example
● Write the equation of the line that goes
through the points (3, 2) and (5, 4).
y2 − y1
m= ( y − y1 ) = m( x − x1 )
x2 − x1
4− 2 ( y − 2) = 1( x − 3)
m=
5−3 y−2= x−3
2
m = =1 y = x −1
2

14. 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.

15. 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)
y2 − y1
Slope: m=
x2 − x1
y = mx + b
2−0 2
m= y = − x+2
0−3 3
2 −2
m= =
−3 3