# 5.6A point-slope formula given a point and slope ```Bell Work
1/8/15
Write the equation of the line described below.
1.
m   3, b  4
2.
m 
1
2
3.
4.
, b  3
Next Chapter
Chapter 5B
Linear Functions II
4/10/2015
5 .6 A
Point-Slope Form
(given a point and slope)
TSWBAT: write an equation given a
point and the slope using the
Point-Slope formula.
Students verify that a point lies on a line, given
an equation of the line. Students are able to
derive linear equations by using the point-slope
formula.
Notes
Graph the line with the given slope that contains the given point.
Find the y-intercept and then write the equation of the line.
Ex.
1
  4, 1  , m 
2
1
m
2
b  3
y  mx  b
1
y    x  3
2
y
1
2
x3

Notes
Now you try.
Graph the line with the given slope that contains the given point.
Find the y-intercept and then write the equation of the line.
Ex.
 2,
 2  , m  3
m  3
b  4
y  mx  b
y   3 x   4
y  3 x  4

Notes
• Point-Slope Form
y  y 1  m  x  x1 
m  slope
 x1 ,
y1   point
It’s called the PointSlope Formula
because you need a
point and the slope to
write the equation of
the line.
Before we were given the graph,
and told to find the equation.
Now we will be given a point and the slope,
and told to find the equation.
Notes
Write the equation of the line.
Ex. x1 y1
 2, 7  , m  3
y  y 1  m  x  x1 
y   7   3  x   2 
Now you try.
Ex. x1 y1
4, 3 points.
, m 2
Labelyour
y  every
y1  mtime.
Write this
 x  x1 
Plug in
y the
 3values.
  2  x   4 
y  7  3 x  2
Distribute.
y  3  2 x  4
y  7  3x  6
7
7
Get y byyitself.
 3  2x  8
3
3
y  3x  1
y  2x  5
Notes
Write the equation of the line.
Ex. x1 y1
  1, 8  , m  4
y  y 1  m  x  x1 
y   8   4  x   1 
Now you try.
Ex. x1 y1
2, points.
4, m  3
Label your
y every
y1  m
Write this
time.
 x  x1 
Plug iny the
 values.
4  3  x   2  
y  8  4  x  1
Distribute.
y  4  3 x  2
y  8  4x  4
8
8
Get y by itself.
y  4  3x  6
4
4
y  4 x  12
y  3 x  10
Notes
Write the equation of the line.
Ex. x1 y1
 4,  3  , m   2
y  y 1  m  x  x1 
y   3   2  x   4

Now you try.
Ex. x1 y1
 4, points.
 7  , m  1
Label your
y every
y1  time.
m  x  x1 
Write this
Plug inythe
7   1 x   4 
 values.
y  3  2  x  4 
Distribute.
y  7  1 x  4 
y  3  2 x  8
3
3
Get y by itself.
y  7   1x  4
7
7
y  2 x  5
y   x  11
Notes
Write the equation of the line.
Ex. x1 y1
1
  6, 7  , m 
3
y  y 1  m  x  x1 
1
y   7    x   6 
3
1
y  7   x  6
3
1
1
y7  x2
3
7
7
y
1
3
x9
Now you try.
Ex. x1 y1
5
Label 4,
your
 3points.
, m 
2
Write ythis
time.
 yevery

m
 x  x1 
1
5
Plug in the values.
y   3   x   4  
2
5
Distribute.
y  3   x  4
Get y by itself. 2
1
5
y  3  x  10
2
3
3
y
5
2
x  13
Notes
Write the equation of the line.
Ex. x1 y1
1
 8,  6  , m  
4
y  y 1  m  x  x1 
1
y   6    x   8  
4
1
y  6    x  8
4
1
1
y6 x2
4
6
6
y
1
4
x4
Now you try.
Ex. x1 y1
4
Label your
points.
 6, 
1 , m  
3
Write this
y every
y  time.
m xx
1

1

Plug in the values. 4
y   1    x   6 
3
4
Distribute.
y 1    x  6
3
Get y by itself.
1
4
y 1   x  8
3
1
1
y
4
3
x9
Summary
point and
To find the equation of a line given a _____
slope formula. Plug in the
the slope use the point-_____
formula Next simplify the expression
values into the ________.
and get y by _____
itself on the left side. Sometimes you need
change change.
to do leave, _______,
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
Homework
5.6A
Write the equation of the line.
1.
1, 6  ,
4.
 3,
7.
9.
 3,
m 2
2.
  2, 1  ,
m 3
3.
 3,
 9  , m  4
5.
  2, 7  ,
m  3
6.
  5,
 1 , m 
  8,
1
8.
  4,
 3 , m  2
 10  , m 
3
 6, m  
4
3
 5, m  
1
4
10.
 6,
 2  , m  1
2
3
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Write the equation of the line.
  2, 7  ,
m  3
```