1. 2.4 Essential Questions What is the point-slope form?
How do you write an equation if you are given a slope and y-intercept?
How do you write an equation if you are given a point and a slope?
How do you write an equation that is parallel or perpendicular to a given line if you are only given a point?
How do you write an equation if you are given two points?

2. 2.4 Write Equations of Lines
Point-slope form
Slope – intercept form
y = mx + b
y – y1 = m(x – x1)

3. Writing an equation given the slope and y-intercept
Write an equation of the line shown.
From the graph, you can see that the slope is m = and the y-intercept is b = – 2. 3 4
y = mx + b
Use slope-intercept form.
y = x + (– 2) 3 4
Substitute for m and –2 for b. 3 4 3 4
y = x – 2
Simplify.

4. Writing an equation given the slope and y-intercept
m = 3, b = 1
Use slope – intercept form
y = mx + b
y = x + 1 3
y = x + 1 3

5. Writing an equation given the slope and y-intercept
GUIDED PRACTICE
m = – 2 , b = – 4
y = mx + b
y = – 2x + (– 4 )
y = – 2x – 4

6. Writing an equation given the slope and y-intercept
GUIDED PRACTICE
m = – b = 3 4 7 2
y = mx + b
y = – x + 3 4 7 2

7. Writing an equation given the slope and a point
EXAMPLE 2
Writing an equation given the slope and a point
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.
y – y1 = m(x – x1)
point-slope form.
Let (x1, y1) = (5, 4) and m = – 3.
y – 4 = – 3(x – 5)
y – 4 = – 3x + 15
y = – 3x + 19

8. Writing an equation given the slope and a point
GUIDED PRACTICE
GUIDED PRACTICE
Write an equation of the line that passes through (– 1, 6) and has a slope of 4.
y – y1 = m(x – x1)
y – 6 = 4(x – ( – 1))
y – 6 = 4x + 4
y = 4x + 10

9. How to write equations of parallel or perpendicular lines
EXAMPLE 3
(use the point-slope form)
Write an equation of the line that passes through (–2,3)
and is parallel to the line y = –4x + 1.
The given line has a slope of m = –4.
So, a line parallel to it has the same slope of –4.
Now 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.
y – y1 = m2(x – x1)
y – 3 = – 4(x – (– 2))
y – 3 = – 4(x + 2)
y – 3 = – 4x – 8
y = – 4x – 5

10. How to write equations of parallel or perpendicular lines
EXAMPLE 3
How to write equations of parallel or perpendicular lines
Write an equation of the line that passes through (–2,3)
and is perpendicular to the line y = –4x + 1. 1 4
A line perpendicular to a line with slope m = – 4 has a slope of
y – y1 = m2(x – x1)
y – 3 = (x – (– 2)) 1 4
y – 3 = (x +2) 1 4
y – 3 = x + 1 4 2
y = x + 1 4 2

11. How to write equations of parallel or perpendicular lines
GUIDED PRACTICE
GUIDED PRACTICE
Write an equation of the line that passes through (4, –2)
and is parallel to the line y = 3x – 1.
A parallel slope would be 3.
y – y1 = m2(x – x1)
y – (– 2) = 3(x – 4)
y + 2 = 3(x – 4)
y + 2 = 3x – 12
y = 3x – 14

12. How to write equations of parallel or perpendicular lines
GUIDED PRACTICE
Write an equation of the line that passes through (4, –2)
and is perpendicular to the line y = 3x – 1. 1 3
A perpendicular slope is –
y – y1 = m2(x – x1)
y – (– 2) = – (x – 4) 1 3
y + 2 = – (x – 4) 1 3 4 3
y + 2 = – x + 1
y = – x – 1 3 2

13. How to write an equation given two points
Write an equation of the line that passes through (5, –2) and (2, 10).
First, find the slope
y2 – y1
m =
x2 –x1 =
10 – (– 2)
2 – 5 12
– 3 =
= – 4
Now you know the slope and two points on the line, so use point-slope form with either given point to write an equation of the line.
y2 – y1 = m(x – x1)
y – 10 = – 4(x – 2)
y – 10 = – 4x + 8
y = – 4x + 18

14. How to write an equation given two points
GUIDED PRACTICE
GUIDED PRACTICE
Write an equation of the line that passes through the given points.
(– 2, 5), (4, – 7)
Find the slope m
– 7 – 5 =
4 – (– 2)
= – 2
Use that slope and one of the two points to find the equation of the line.
y – y1 = m(x – x1)
y – 7 = – 2(x – 4)
y – 7 = – 2 (x – 4)
y + 7 = – 2x + 8
y = – 2x + 1

15. How to write an equation given two points
GUIDED PRACTICE
GUIDED PRACTICE
Write an equation of the line that passes through
(6, 1), (–3, –8)
m =
– 8 – 1
– 3 – 6
– 9 =
= 1
y – y1 = m(x – x1)
y – (– 8)) = 1(x – (– 3))
y + 8 = 1 (x + 3)
y + 8 = x + 3
y = x – 5

16. How to write an equation given two points
GUIDED PRACTICE
Write an equation of the line that passes through
(–1, 2), (10, 0)
m =
0 – 2
10– (– 1) 2 11 = –
y – y1 = m(x – x1)
y – 0 = (x – 10) 2 11 –
y = (x – 10) 2 11 –
y = 2 11 –
x + 20

17. HOMEWORK 2.4
p. 101 #3-16(EOP); 17, 20-25,
30-38, 40-45