1. y = mx + b y – y1 = m (x – x1) Topic: Writing Equations given two
points
Text Section: 5.2
Standard: 7.0
Question /
Key Words
Notes or Solutions to Problems
m = Slope
b = y-intercept
Slope-Intercept
Form
y = mx + b
m = Slope
Point–Slope
y – y1 = m
(x – x1)
Form
Point

2. -1 – – y – y1 = m (x – x1) y – 1 = -1 (x – ) 2 y – 1 = -1x + 2 + 1 + 1
Question /
Key Words
Notes or Solutions to Problems
Step 1: Find the Slope
Write in
slope-intercept form
the equation of the line
that passes through
the points (2, 1) and
(-5, 8).
y2 – y1
Slope (m) =
x2 – x1 – 7 8 1 m -1 = = = – -5 2 -7
(x1, y1)
Step 2: Write in Point Slope Form
(x2, y2)
y – y1 = m
(x – x1)
y – 1 = -1
(x – ) 2 y
– 1 =
-1x
+ 2
+ 1
+ 1 y = -x
+ 3

3. – – y – y1 = m (x – x1) y – (-4) = 3 (x – ) 2 y + 4 = 3x – 6 – 4 – 4 y
Question /
Key Words
Notes or Solutions to Problems
Step 1: Find the Slope
2) Write in
slope-intercept form
the equation of the line
that passes through
the points (2, -4) and
(4, 2).
y2 – y1
Slope (m) =
x2 – x1 2 –
(-4) 6 2
+ 4 m = = = = 3 – 4 2 2 2
(x1, y1)
Step 2: Write in Point Slope Form
(x2, y2)
y – y1 = m
(x – x1)
y –
(-4) = 3
(x – ) 2 y
+ 4 = 3x
– 6
– 4
– 4 y = 3x
– 10

4. – – y – y1 = m (x – x1) y – 3 = (x – ) (-7) y – 3 = (x ) + 7
Question /
Key Words
Notes or Solutions to Problems
Step 1: Find the Slope
3) Write in
slope-intercept form
the equation of the line
that passes through
the points (-7, 3) and
(-4, 1).
y2 – y1
Slope (m) =
x2 – x1 1 – 3 -2 -2 2 m = = = = – – -4
(-7) -4
+ 7 3 3
(x1, y1)
Step 2: Write in Point Slope Form
(x2, y2)
y – y1 = m
(x – x1) 2
y – 3 = –
(x – )
(-7) 3 2
y – 3 = –
(x )
+ 7 3

5. y – 3 = (x ) + 7 y – 3 = x – + + 3 + 3 y = x 3) Write in
Question /
Key Words
Notes or Solutions to Problems
3) Write in
slope-intercept form
the equation of the line
that passes through
the points (-7, 3) and
(-4, 1). 2
y – 3 = –
(x )
+ 7 3 2 14 y
– 3 = – x – 3 3
(x1, y1) 9 +
+ 3
+ 3 3
(x2, y2) 2 5 y = – x – 3 3

6. – – y – y1 = m (x – x1) y – (-9) = (x – ) (-2) y + 9 = (x ) + 2
Question /
Key Words
Notes or Solutions to Problems
Step 1: Find the Slope
4) Write in
slope-intercept form
the equation of the line
that passes through
the points (-2, -9) and
(6, -3).
y2 – y1
Slope (m) =
x2 – x1 -3 –
(-9) 6 -3
+ 9 3 m = = = = – 6
(-2) 6
+ 2 8 4
(x1, y1)
Step 2: Write in Point Slope Form
(x2, y2)
y – y1 = m
(x – x1) 3
y –
(-9) =
(x – )
(-2) 4 3 y
+ 9 =
(x )
+ 2 4

7. y + 9 = (x ) + 2 y + 9 = x + – – 9 – 9 y = x y = x 4) Write in
Question /
Key Words
Notes or Solutions to Problems
4) Write in
slope-intercept form
the equation of the line
that passes through
the points (-2, -9) and
(6, -3). 3
y + 9 =
(x )
+ 2 4 3 6 y
+ 9 = x + 4 4
(x1, y1) 36 –
– 9
– 9 4
(x2, y2) 3 30 y = x – 4 4 3 15 y = x – 4 2

8. y = mx + b y b = -2 -4 x +2 1 m = = – + 2 -4 2 1 y = – x – 2 2
Question /
Key Words
Notes or Solutions to Problems
5) Write an equation in
slope-intercept form of
the line shown in the
graph
Write in slope-intercept form.
y = mx + b y
Find the y-intercept. b = -2
Find the slope m. -4 x +2 1
m = = –
+ 2 -4 2 1 y = – x
– 2 2

9. y = mx + b x1 = y1 = y – y1 = m (x – x1) y – (-2) = (x – ) 2 y + 2 =
Question /
Key Words
Notes or Solutions to Problems
6) Write an equation in
slope-intercept form of
the line shown in the
graph
Write in slope-intercept form.
y = mx + b
Find the slope m. +2 2 y
m = = +3 3
Find a point.
x1 =
y1 =
(2, -2) 2 -2
Write in Point Slope Form x
y – y1 = m
(x – x1) +3 2 +2
y –
(-2) =
(x – ) 2 3 2 y
+ 2 =
(x )
– 2 3

10. y + 2 = (x ) – 2 y + 2 = x – – – 2 – 2 y = x 2 3 y 2 4 3 3 6 x 3 +3 +2
Question /
Key Words
Notes or Solutions to Problems
6) Write an equation in
slope-intercept form of
the line shown in the
graph
Write in Point Slope Form 2 y
+ 2 =
(x )
– 2 3 y
Write in Slope-Intercept Form 2 4 y
+ 2 = x – 3 3 6 – x
– 2
– 2 3 +3 +2 2 10 y = x – 3 3

11. y = mx + b x1 = y1 = y – y1 = m (x – x1) y – 1 = – (x – ) 2 +1 1 m = =
Question /
Key Words
Notes or Solutions to Problems
7) Write an equation in
slope-intercept form of
the line shown in the
graph
Write in slope-intercept form.
y = mx + b
Find the slope m. +1 1
m = = – y –4 4
Find a point.
x1 =
y1 =
(2, 1) 2 1
– 4 +1
Write in Point Slope Form
y – y1 = x m
(x – x1) 1
y – 1 = –
(x – ) 2 4

12. y – 1 = – (x – ) 2 y – 1 = – x + + + 1 + 1 y = – x y = – x 1 4 y 1 2
Question /
Key Words
7) Write an equation in
slope-intercept form of
the line shown in the
graph
Write in Point Slope Form 1
y – 1 = –
(x – ) 2 4 y
Write in Slope-Intercept Form 1 2 y
– 1 = – x +
– 4 +1 4 4 4 +
+ 1
+ 1 4 x 1 6 y = – x + 4 4 1 3 y = – x + 4 2

13. Assignment
Book Pg. 288 – 289
# 3, 5, 7, 8, 21, 22, 23, 25 – 31 odd, 35