1. y – y1 = m (x – x1) Topic: Writing Equations in Point-Slope Form
Text Section: 5.4
Standard: 8.EE.6
To write linear equations given
a point and a slope
Objective:
The point-slope form of the equation of the line.
Through (x1, y1) with slope is
Point–Slope
y – y1 = m
(x – x1)
Form

2. y – y1 = m (x – x1) x1 = y1 = y – 4 = (x – ) y +3 3 m = = +4 4 3 4 3 x
Question /
Key Words
Notes or Solutions to Problems
Write an equation
of the line in the
graph point-slope
form.
Point-Slope form
y – y1 = m
(x – x1)
From the graph by the slope. y +3 3
m = = +4 4 +4 +3
From the graph (x1, y1).
x1 =
y1 = 3 4
(3, 4) 3
y – 4 =
(x – ) x 3 4

3. y – y1 = m (x – x1) x1 = y1 = y – 2 = – (x – ) (-1) y – 2 = – (x ) +2
Question /
Key Words
Notes or Solutions to Problems
2) Write an equation
of the line in the
graph point-slope
form.
Point-Slope form
y – y1 = m
(x – x1)
From the graph by the slope. +2 2
m = = – -3 3 –3
(-1, 2) +2
From the graph (x1, y1). x
x1 =
y1 = -1 2 2
y – 2 = –
(x – )
(-1) 3 2
y – 2 = –
(x )
+ 1 3

4. y – y1 = m (x – x1) x1 = y1 = y – 1 = (x – ) y – 1 = x +1 1 m = = +2 2
Question /
Key Words
Notes or Solutions to Problems
3) Write an equation
of the line in the
graph point-slope
form.
Point-Slope form
y – y1 = m
(x – x1)
From the graph by the slope. +1 1
m = = +2 2 +2 +1
From the graph (x1, y1).
(0, 1) x
x1 =
y1 = 1 1
y – 1 =
(x – ) 2 1
y – 1 = x 2

5. y – y1 = m (x – x1) x1 = y1 = y – (-4) = 5 (x – ) 2 y + 4 = 5 (x – ) 2
Question /
Key Words
Notes or Solutions to Problems
4) Write in
point-slope form
the equation of the line
that passes through
the point (2, -4)
with slope 5.
Point-Slope form
y – y1 = m
(x – x1)
m = 5
x1 = 2
(x1, y1)
y1 = -4
m = 5
y –
(-4) = 5
(x – ) 2 y
+ 4 = 5
(x – ) 2

6. y – y1 = m (x – x1) x1 = y1 = y – (-5) = -6 (x – ) (-3) y + 5 = -6
Question /
Key Words
Notes or Solutions to Problems
5) Write in
point-slope form
the equation of the line
that passes through
the point (-3, -5)
with slope -6.
Point-Slope form
y – y1 = m
(x – x1)
m = -6
x1 = -3
(x1, y1)
y1 = -5
m = -6
y –
(-5) = -6
(x – )
(-3) y
+ 5 = -6
(x )
+ 3

7. y – y1 = m (x – x1) y – 5 = -3 (x – ) (-2) y – 5 = -3 (x ) + 2 y = mx
Question /
Key Words
Notes or Solutions to Problems
Point-Slope form
6) Write in
Slope-Intercept form
the equation of the line
that passes through
the point (-2, 5)
with slope -3.
y – y1 = m
(x – x1)
y – 5 = -3
(x – )
(-2)
y – 5 = -3
(x )
+ 2
(x1, y1)
Slope-Intercept form
m = -3 y = mx
+ b y
– 5 = -3
(x )
+ 2 y
– 5 =
-3x
– 6
+ 5
+ 5 y =
-3x
– 1

8. y – y1 = m (x – x1) y – (-1) = 5 (x – ) 2 y + 1 = 5 (x ) – 2 y = mx
Question /
Key Words
Notes or Solutions to Problems
Point-Slope form
7) Write in
Slope-Intercept form
the equation of the line
that passes through
the point (2, -1)
with slope 5.
y – y1 = m
(x – x1)
y –
(-1) = 5
(x – ) 2 y
+ 1 = 5
(x )
– 2
(x1, y1)
Slope-Intercept form
m = 5 y = mx
+ b y
+ 1 = 5
(x )
– 2 y
+ 1 = 5x
– 10 –1
– 1 y = 5x
– 11

9. m = -3 m = -3 x1 = y1 = y – y1 = m (x – x1) y – (-5) = -3 (x – ) 1 y
Question /
Key Words
Notes or Solutions to Problems
8) Write in
slope-intercept form
the equation of the line
that is parallel to the
given line y = -3x +2
and passes through the
point (1, -5)
The answer must look like y = mx + b
(slope-intercept form)
Line 1
Line 2
m = -3
m = -3
x1 =
y1 = 1 -5
m = -3
y = -3x + 2
y – y1 = m
(x – x1)
(x1, y1)
y –
(-5) = -3
(x – ) 1 y
+ 5 = -3
(x )
– 1 y
+ 5 =
-3x
+ 3
– 5
– 5 y =
-3x –2

10. m = m = x1 = y1 = y – y1 = m (x – x1) y – 1 = (x – ) 3 y – 1 = x + 1
Question /
Key Words
Notes or Solutions to Problems
9) Write in
slope-intercept form
the equation of the line
that is parallel to the
given line y = x + 2
and passes through the
point (3, 1)
The answer must look like y = mx + b
Line 1
Line 2 1
m = 1
m = 2 2
x1 =
y1 = 3 1 1 2
y – y1 = m
(x – x1) 1
m = 1 2 y = x + 2 2
y – 1 = 1
(x – ) 3
(x1, y1) 2 1 3 y
– 1 = x – 2 2
+ 1 +1 y = 1 1 x – 2 2

11. m = m = x1 = y1 = y – y1 = m (x – x1) y – 2 = (x – ) (-4) y – 2 = (x )
Question /
Key Words
Notes or Solutions to Problems
10) Write in
slope-intercept form
the equation of the line
that is parallel to the
given line y = x + 5
and passes through the
point (-4, 2)
Line 1
Line 2 2
m = 2
m = 3 3
x1 =
y1 = -4 2
y – y1 = m
(x – x1) 2 3 2
m =
y – 2 = 2
(x – )
(-4) 3 3 2 y
– 2 =
(x )
+ 4
(x1, y1) 3 2 8 y
– 2 = x + 3 3
+ 2 +2 y = 2 14 x + 3 3

12. m m = 2 x1 = y1 = m y – y1 = m (x – x1) y – 3 = 2 (x – ) 1 y – 3 = 2x
Question /
Key Words
Notes or Solutions to Problems
11) Write in
slope-intercept form the
equation of the line that is
parallel to the line in the
graph and passes through
the given point.
The answer must look like y = mx + b
(slope-intercept form)
Line 1
Line 2 +2 m
m = 2 = +1
(1, 3) y x
x1 =
y1 = 1 3 m = 2
y – y1 = m
(x – x1)
y – 3 = 2
(x – ) 1 y
– 3 = 2x
– 2
+ 3
+ 3 +1 y = 2x
+ 1 +2

13. m m = – m – x1 = y1 = y – y1 m (x – x1) = Line 1 Line 2 +1 1 = -3 3 1
Question /
Key Words
Notes or Solutions to Problems
12) Write an in
slope-intercept form the
equation of the line that is
parallel to the line in the
graph and passes through
the given point.
The answer must look like y = mx + b
(slope-intercept form)
Line 1
Line 2 +1 m 1 =
m = – -3 3 y x 1
(-3, -1) m – = 3
x1 =
y1 = -3 -1 -3
y – y1 m
(x – x1) = +1 1
y –
(-1) = –
(x – )
(-3) 3 1 y
+ 1 = –
(x )
+ 3 3

14. y + 1 = – x 1 – 1 – 1 y = – x – 2 Line 1 Line 2 1 y + 1 = – (x ) + 3 3
Question /
Key Words
Notes or Solutions to Problems
12) Write an in
slope-intercept form the
equation of the line that is
parallel to the line in the
graph and passes through
the given point.
The answer must look like y = mx + b
(slope-intercept form)
Line 1
Line 2 y x 1 y
+ 1 = –
(x )
+ 3 3 y
+ 1 = – 1 x – 1 3 -3
– 1
– 1 +1 y = – 1 x
– 2 3