Download Point-Slope Form!

Writing Equations
in
Point-Slope Form
Algebra 1
Glencoe McGraw-Hill
JoAnn Evans
Today we’re going to learn to use the
Point-Slope form of the equation of a line.
y – y1 = m(x – x1)
Do any parts of this equation look
familiar to you?
..
(x, y)
(3, 4)
Write an expression for the
slope between the two points.
Clear the fraction. Multiply
both sides by (x – 3).
Symetric Property
This equation is written in
Point-Slope form.
This graph shows a line
with a slope of 2.
y4
m
x3
y4
2
x3
 ( y  4) 
2(x  3)  
(x  3)
 (x  3) 
2(x  3)  y  4
y  4  2(x  3)
y coordinate
slope
x coordinate
y  y1  m(x  x1 )
 m represents the slope of the line
 (x1, y1) represents a known point on the line
 (x, y) represents any other point on the line
m, x1, and y1 will be replaced by numbers.
x and y will be the variables.
Use the point-slope form to write the equation of
the line passing through the point (-1,
3) with a
-1 3
slope of -2.
-2
y  y1  m(x  x1 ) Point-slope form
y  3  2x  (1)
y  3  2(x  1)
The point-slope form has two
subtraction signs in it. Don’t
forget to include them if either
x1 or y1 are negative numbers.
Write the equation of
the line passing through
the point (0, 7) with a
slope of 12.
Write the equation of
the line passing through
the point (-3, -4) with a
slope of -2.
y  y1  m(x  x1 )
y  y1  m(x  x1 )
y  7  12(x  0)
y  (4)  2x  (3)
y  7  12x
When you’re asked to put
an equation in Point-Slope
form, don’t distribute the
slope and isolate the y!
y  4  2(x  3)
Remember… in Point-Slope
form, don’t distribute the
slope and isolate the y!
Write the equation of
Write the equation of
the line passing through
the horizontal line
the point (-2, 0) with a
3

slope of
.
2
passing through the
y  y1  m(x  x1 )
3
y  0   x  ( 2) 
2
3
y  0   (x  2)
2
point (0, 5).
y  y1  m(x  x1 )
y  (5)  0(x  0)
y5 0
Horizontal lines have
a slope of 0!
Change From Point-Slope to Slope-Intercept Form:
Write an equation of the line that passes through the
point (6, -8) with slope of -4.
Then simplify the result to the slope-intercept form.
y  y1  mx  x1 
y  ( 8)  4x  (6) 
y  8  4x  6
y  8  4x  24
8
8
y  4x  16
Point-Slope equation
Substitute -4 for m, 6 for
x1, and -8 for y1
Point-Slope Form!
Simplify and distribute
Subtract 8 from
both sides
Slope-Intercept Form!
Write an equation of the line that passes through the point
2
(5, -1) with slope of 3 . Then simplify the result to the
slope-intercept form.
y  y1  mx  x1 
2
y  ( 1)  x  (5) 
3
2
y  1  x  5 Point-Slope Form!
3
2
10
y1  x
3
3
1
1
2
13
y  x
3
3
Slope-Intercept Form!
Change From Point-Slope Form to Standard Form:
Write the equation y + 6 = -3(x – 4) in standard form.
y  6  3(x  4)
Write the equation.
y  6  3x  12
6
6
Distribute the slope.
y  3x  6
3x  y  6
Subtract 6 from both sides.
Add 3x to both sides.
Standard Form!
Change From Point-Slope Form to Standard Form:
5
Write the equation y  5   (x  2) in standard form.
4
5
y  5   (x  2)
4
Write the equation.
5

4( y  5)  4  (x  2) Multiply each side by 4 to
clear the fraction.
 4
4y  20  5(x  2)
4 y  20  5x  10
4 y  5x  10
5x  4 y  10
Subtract 20 from each side.
Add 5x to both sides.
Standard Form!
Acme Moving Company charges a set daily fee for
renting a moving truck, plus a charge of $0.50 per
mile driven. It cost Jordan $64 to rent the truck on
a day when he drove a total of 48 miles.
Write an equation in point-slope form to find the total fee,
y, for any number of miles, x, that the truck is driven.
What number represents
a rate of change?
$0.50 per mile
The instructions tell us
that x will represent
the number of miles and
y will represent the
total cost.
(x, y)
This is the slope. (m)
(48, 64)
The # of miles is 48.
The cost is $64.
Acme Moving Company charges a set daily fee for
renting a moving truck, plus a charge of $0.50 per
mile driven. It cost Jordan $64 to rent the truck on
a day when he drove a total of 48 miles.
We have enough
information now to
write an equation in
point-slope form.
Change the equation from
point-slope form to slopeintercept form.
What is the daily fee to
rent a truck?
m = 0.50
(48, 64)
y  y1  m(x  x1 )
y  64  0.50(x  48)
y  64  .50x  24
64
64
y  .50x  40
In 1908 the average movie ticket cost $0.05!
100 years later in 2008 the average movie ticket cost
$8.50!
Use this information to write the point-slope form of an equation
to find the cost of a movie ticket, y, for any year, x.
In 1908:
(year, cost)
(0, 0.05)
In 2008:
(year, cost)
(100, 8.50)
Find the slope between the points: (100, 8.50)
(0, 0.05)
8.45
8.50  0.05
 .0845

m
100
100  0
m  .0845
What does this mean?
This is the rate of change for the cost
of a movie ticket over that period of
100 years. The cost rose, on average,
8.45 cents per year.
Use the slope and one of the
points to write an equation in
y  y1  m(x  x1 )
point-slope form.
Use (100, 8.50)
y  8.50  .0845(x  100)
y  8.50  .0845x  8.45
Change this equation to
slope-intercept form.
y  .0845x  .05
Rate of change
per year.
Cost of a movie
in year 0.
Use the equation to predict the price of
a movie ticket 10 years from now.
10 years from now it will
be 110 years since the 0
year. Substitute 110 for
the year.
y  .0845x  .05
y  .0845(110)  .05
y  9.295  .05
y  9.345
If tickets keep rising at the same rate, it should
cost about $9.35 to see a movie in 2018.