Download Finding the equation of a line. - mathemons

Finding the
equation of a
line.
POINT-SLOPE FORM
y – y1 = m ( x – x1 )
Bell Work
Using the point-slope form, find the equation
of the line with the given conditions. Express
your answer in y=mx + b.
1.
2.
3.
4.
5.
Having a slope of 3 and passing through
the point ( 4, 5 ).
Having a slope of -2 and passing through
the point ( - 1, 6 )
m = 8 , ( 7, 4 )
m = -10 , ( 6, -8 )
m=5,(9,3)
Take Note
If
the given is the slope and a
point on the line, we can use
the point-slope form which is.

y – y1 = m ( x – x1 )
What if the given slope is a
fraction?
Try
this!
Find the equation of the line
having a slope of ¾ and
passing through ( 2, 5 ).
Solution
Given : m = ¾ and passing
through ( 2,5 )
y – y1 = m ( x – x1 )
y–5=¾(x–2)
y – 5 = ¾ x – 6/4
y = ¾ x – 6/4 + 5
y = ¾ x + 7/2
Another solution
m = ¾ and passing through ( 2, 5 )
y – y1 = m ( x – x1 )
y–5=¾(x–2)
4(y–5)=3(x–2)
4y – 20 = 3x – 6
4y = 3x – 6 + 20
4y = 3x + 14
4
4
4
y = ¾ x + 7/ 2
Try this!
Find the equation of the
line having the slope of
½ and passing through
( - 3, 4 )
Try this!
Find the equation of the
line having a slope of
2/5 and passing through
( - 3, - 6 )
Try this!
Find the equation of the
line having a slope of
-2/7 and passing
through ( - 1, - 4 )
Think – Pair - Share
Find the equation of the line given
the slope and a point.
1.
2.
3.
4.
5.
m = 2/3 ( 4, 7 )
m = ¼ ( 3, 1)
m = 3/5 ( -2, 4)
m = - 1/8 ( 3, -2)
m=½
( 0, -23 )
Finding Slopes and
y - intercepts from
Equations
y = mx + b
Objectives:
Change
a linear equation to
the form y = mx + b.
Determine
the slope of a line
and the y-intercept from the
given equations.
Thoughts to Ponder
To
determine the slope and
y – intercept from a given equation,
solve the equation for y in terms of x
and express the resulting equation in the
form y = mx + b. The coefficient of the xterm is the slope (m) and the constant
term b represents the y-intercept.
Example:
Find
the slope of the line and yintercept of 8x + y = 10.
Solution:
Given: 8x + y = 10
y = mx + b
y = -8x + 10
Therefore the slope is -8 and the yintercept is 10.
Example
Find the slope and y-intercept in
the line 2x + 2y = 12
Solution:
2x + 2y = 12
2y = -2x + 12
2
2
2
y = -x + 6
Slope = -1 : y-intercept = 6
Try this!
Change 3y + 15 = 3x
in y-form.
Try this!
Change 2y + 6x = 30
in y-form.
Board Drill
Change
the following equations in
the form y = mx + b.
10 x + y = 3
2x – 2y = 6
10x + 5y = 25
14 x- 7y = -12
2y – 4 = 35 – x
Seatwork
Change the following equations in the form y =
mx + b, then determine the slope and yintercept.
Given
1. 9x + y = 18
2. 6x + 2y = 20
3. 3y + 5x = 2y + 2
4. 3x + 6y = -21
5. 2x + 3y = 15
Y-form
slope
Y-intercept
Standard Form
of Linear
Equations
Ax + By = C
Mathematical Concepts
Standard
This
Form Ax + By = C
is one of the two forms of a
linear equation. The letters A, B,
and C represent numbers. The
numbers may not be fractions.
Examples
1.
Change the equation y = -2x + 5 in
Standard Form
Given: y = -2x + 5
Solution: Just put all the variable terms on
the left side of the equation.
Note: x – term must comes first
Answer:
2x + y = 5
Examples
2. Change the equation y = 3x - 8 in Standard
Form
Given: y = 3x - 8
Solution: Just put all the variable terms on
the left side of the equation.
Note: the value of a should always be
positive
-3x + y = -8
-3x + y = -8 Multiply by -1
3x – y = 8
Examples
3. Change the equation y = -2/3x - 7 in
Standard Form
Given: y = -2/3 x - 7
Solution: Just put all the variable terms on
the left side of the equation.
Note: there must be no fractions in A, B, or C
2/3 x + y = -7
2/3 x + y = -7
Multiply by 3
2x + 3y = -21
Board Drill
Write the following in standard form.
y = 6x - 9
Board Drill
Write the following in standard form.
3x – 5 = 2y
Board Drill
Write the following in standard form.
7 = 2x – 3y
Board Drill
Write the following in standard form.
y = -3/4x -10
Board Drill
Write the following in standard form.
y = ½ x -7
Seatwork
Write the following equations in standard form.
y = -8x + 5
2. y = 10x + 2
3. 3x – 6 = 7y
4. y = 1/3 x – 5
5. y = -4/9 x + 3
1.
Drills
Group A:
-3/5 x – 7y = 11
Group B
y = 8x - 13
Group C
5 + 4x = y
Drills
Group A:
-4/7 x – 2y = 3
Group B
y = 9x + 2
Group C
y = -2x - 7
Drills
Group A:
-3/8 x – y = 7
Group B
y = -1/2 x + 9
Group C
y = 3x - 4
Did you know that?......
Using the Standard Form of Linear Equation we can
also determine the value of the slope and yintercept using the formula.
SLOPE =
−𝑨
𝑩
Y-INTERCEPT =
𝑪
𝑩
Change the equation in standard form
then find the values of a, b, and c
3x = 5y + 2
S. F 3x – 5y = 2
A=3
B = -5
C=2
Change the equation in standard form
then find the values of a, b, and c
y = 3x – 7
-3x + y = -7 Multiply by -1
3x – y = 7
Therefore: A = 3
B = -1
C=7
Change the equation in standard form
then find the values of a, b, and c
3/4x = y – 7
¾ x – y = -7
4 ( ¾ x – y = -7)
3x – 4y = -28
Therefore:
A=3
B = -4
C = -28
Think-Pair-Share
Complete the table below.
Given
1. y = -4x + 5
2. y = 2x -7
3. 2x = 5 – 9y
4. y = 2/3x - 5
5. 7y = -4/9 x - 3
S.F
A
B
C
m
b